David Davies, Ian Lucas, Albert Owen and Geraint Davies are hoping to win the support of other MPs to take on the role at the heads of committees that scrutinise government departments.
The role pays Â£15,000 on top of an MP's basic salary.
Monmouth Tory MP David Davies is so far the only declared candidate to remain Welsh Affairs Committee chair.
He has held the post since 2010.
North Wales Labour MPs Mr Lucas and Albert Owen are battling it out to chair the Business, Energy and Industrial Strategy committee but face competition from former Labour frontbencher Rachel Reeves.
Swansea West MP Mr Davies is standing to chair the Transport Committee.
MPs will vote on the new chairs next Wednesday but the committees are unlikely to be up-and-running until after the long Commons summer recess.
Four Welsh MPs are standing for election as chairs of influential parliamentary committees.