The former Tory MP is said to be agonising about what to do if there is a by-election as a result of the arrest last month of his successor, Dan Norris, on suspicion of rape and child sex offences.
The demands come as Labour MP Dan Norris faces serious sexual abuse allegations and amid claims that another MP committed a sex assault before being elected.
Dan Norris, who ousted Jacob Rees-Mogg as MP for North East Somerset at last year's election, was taken into custody after police raided his constituency home.