The meeting is reportedly in Wichita.
The Crimson Tide are said to be offering a $3 million per year deal that would be worth around $20 million over the life of the contract.
While Alabama does not have much of a basketball tradition, the school does boast excellent athletic support facilities.
Marshall is also expected to be on the "short list" of candidates to replace former Texas coach Rick Barnes, who was fired over the weekend.
Texas has more money to spend, and can point to a decent basketball history.
Marshall has built a powerhouse in Wichita, leading the Shockers to a pair of Sweet-16's, and one trip to the Final Four, over the past three seasons.
While WSU plays in a smaller conference than either Texas or Alabama, the Shocker program enjoys great support from boosters, including the ultra-wealthy Koch family.
Some Wichita media members say they believe WSU has the money to match any offer Marshall will receive.
They suggest the decision could hinge on whether the coach feels like another school would give him a better chance to achieve his goal of winning the national championship.
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