Joshua's promoter Eddie Hearn has confirmed that American Martin, also undefeated, is a possible opponent for Joshua at London's O2 Arena on 9 April.
Martin, 29, has won 23 and drawn one of 24 fights and beat Vyacheslav Glazkov for the vacant IBF belt in January.
An Olympic gold medallist at London 2012, 26-year-old Joshua has 15 knockouts from 15 professional fights.
He most recently beat Dillian Whyte with a seventh-round knockout to claim the British heavyweight title, the first time he has been taken past the third round.
Tyson Fury was stripped of the IBF world heavyweight title after he opted for a rematch against Ukrainian Glazkov's compatriot Wladimir Klitschko rather than face the mandatory challenger.
Unbeaten British heavyweight Anthony Joshua is in talks over an IBF world title fight against Charles Martin.