Johnson, 25, only joined Crystal Palace from Tottenham for a reported £35 million in January, but has failed to score a single goal in his 26 games.
McNeil, 26, on the other hand, has fallen down the pecking order at Everton and is understood to be keen on a move away for more regular action.
According to The Times, both Palace and Everton may have come up with a solution as they consider a sensational swap deal.
While such deals are often suggested, there hasn’t been a straight swap deal between Premier League clubs since Alexis Sanchez and Henrikh Mkhitaryan in 2018.