This is a loaded question and several issues are involved and need clarification. Here are a few random thoughts that come to mind based on my understanding of giving in the New Testament.
First, we are not now under the Old Testament law or its economy. Further, the church is not Israel and a lot of the giving issues for Israel (the tithes and offerings) involved God’s special program for the theocratic nation and their life in the land of Israel. While we may obviously draw many principles from the Old Testament because all Scripture is ‘profitable,’ all Scripture is not applicable to us as members of the church, the body of Christ. Unfortunately, there is a lot of heresy taught in pulpits in the name of application which often amounts to twisting Scripture to promote an agenda whether personal or corporate.
As an illustration, in the Old Testament they were told to bring the whole tithe into the storehouse (Mal.3:10). Here the Lord appealed to His covenant promises to the nation and challenged Israel to bring the whole tithe into the storehouse so there would be adequate food for the priests. The “storehouse” refers to a special room or rooms in the temple for keeping tithed grain (cf. 1 Kings 7:51; Neh. 10:38; 13:12). By doing this, the people would see that God would open heaven’s floodgates and pour out…blessing on them in accordance with the promised blessing for obedience rather than cursing (discipline) for disobedience as in Deuteronomy, especially chapters 28ff. These blessings would include agricultural prosperity—good crops not destroyed by pests, and undamaged vines (Mal. 3:11)—and a good reputation among all the nations (v. 12). These blessings simply awaited their obedience.
But the church is not Israel, we do not live in the land, we do not have the temple (all believers constitute the temple [1 Cor. 3:15-17; 6:19]), and all believers are priests of God (1 Pet. 2). The church building is not God’s house as was the temple. Believers are the temple. Wherever Christians are gathered together—an airplane hanger, a school building, a home as in the early church—that’s where the Lord is as He indwells us by the Spirit.
Obviously, there are legitimate applications of the Malachi passage, but insisting that believers give all that they give to the local church is, in my opinion, manipulating the passage for our own agendas. Pastors and church leaders want to see the budget grow to meet the needs, so this passage is sometimes used to coerce believers into giving strictly to the church. Perhaps a more biblical application of this passage is that believers should have their spiritual priorities straight, be deeply concerned about the things of God (His purposes, etc.) and support those ministering the things of God, as Paul makes clear in Galatians 6 and 1 Timothy 5. But this needs to be in keeping with New Testament principles—as the Lord directs them by the Spirit—having first given themselves to the Lord (see 2 Cor. 8:5).
Giving for New Testament believers is not a set amount and it is a personal matter that is to proceed from one’s relationship with the Lord, as led by the Spirit. In my opinion and based on 2 Corinthians 8 and 9, there should never be any kind of pressure or coercion to get people to give either a certain percentage or to a certain need. This doesn’t mean a church shouldn’t share the needs (a more adequate salary for a pastor, increased missions support, a building fund, a hurting family) and even encourage believers to prayerfully consider those needs as Paul did in 2 Corinthians 8-9, but this needs to be done in a non-manipulating manner.
The New Testament nowhere tells us that giving to the church is the only way to give to God. If believers are giving to missionaries, para-church organizations, or to people in need, especially to other believers, this is in essence giving to Christ Himself as He tells us. Anything we do for others (giving, hospitality, etc.) is giving to God and expressing His love (see Matt. 25:35-45).
It should not matter where or to whom a pastor is giving. As long as you are confident that he is a spiritual man who is laying up treasures in heaven through his life and in the way he cares and gives to others, etc., this should be your primary concern.
Now, having said that, there are two things I might add. First, if a pastor was giving nothing to the church, then discussing this with him might be in order, but mainly to find out why and to see if he is hurting in some way. Is his salary what it should be? Is it in keeping with what others make in your church according to his age, experience, and his needs? Are you obeying Galatians 6:6, “sharing all good things with the one who teaches”? Is he feeling resentment toward the church or the board for some reason?
Second, one might also want to know if his claim that he is giving elsewhere is a smoke screen (a way to avoid giving). It may be that he is in debt and perhaps buying a lot of things he can’t afford. Then there would be a question regarding his maturity, his basic spiritual walk, and qualification for leadership. Lack of giving, then, would merely be a symptom, and not the real problem.
Finally, believers certainly ought to give to the local church to support it (Gal. 6:6-7) as God has prospered and as each person is persuaded in his or her own mind (1 Cor. 16:1f; 2 Cor. 8-9). This support is for those ministering the Word to you (Gal. 6:6-7, i.e., like your pastor-teacher), and other areas of ministry like missions at home and abroad (see 3 John 5-8), and to those in need (Gal. 6:10, “So then, whenever we have an opportunity, let us do good to all people, and especially to those who belong to the family of faith”).