The President of the Queensland LNP has excoriated MP Trevor Evans for flagging that he could cross the floor to support gay marriage, saying the issue is "peripheral" and MPs should abide by the party's policy.

President Gary Spence's email, sent to LNP members, is being read as a sign that Mr Evans could face a threat to his preselection as the member for the seat of Brisbane.

Trevor Evans.

In the email Mr Spence stressed the LNP's position was to support a plebiscite or a postal ballot and said it was "unfortunate" that some elected LNP MPs have been "contributors" to the media coverage on same-sex marriage by canvassing favouring a private members' bill and free vote in Parliament.

On Monday Mr Evans told News Corp that with the Parliament rejecting the plebiscite, a breakthrough in the stalemate was needed and he did not rule out crossing the floor to help bring on a vote on gay marriage. He also appeared on the ABC's Lateline that evening.