Wealth is never mentioned in the Bible as a qualification for church leadership; in fact, it could even be a barrier if someone has allowed money to become the most important thing in his or her life. The Bible warns that "the love of money is a root of all kinds of evil" (1 Timothy 6:10).
Instead, the Bible stresses that the most important requirement for someone who is called to be a church leader is his or her spiritual commitment and outlook. This isn't true only for the pastor or preacher; it applies to everyone who is given a leadership role in a congregation. After all, how can people strengthen the spiritual life of others if they're spiritually weak themselves?
When the first Christians needed to find leaders who could take care of practical matters, they were told to seek individuals "who are known to be full of the Spirit and wisdom" (Acts 6:3). Leaders also were to be (among other things) "above reproach ... temperate, self-controlled, respectable ... not quarrelsome, not a lover of money" (1 Timothy 3:2-3).
Pray for God's guidance as you seek new leaders for your church - and urge your committee to pray also. Don't exclude from consideration people who are leaders in other areas (like business) - but only if they are committed to Christ and are seeking to serve Him above all else.