Inter Milan have been demanding as much as £50 million for Perisic, however, they have been willing to lower a fee if Martial is included in the exchange.
Jose Mourinho has been a long-term admirer of Perisic, with the Portuguese boss previously confirming his desire to make a fourth signing before the window closes.
Before the official announcement of Nemanja Matic from Chelsea, Mourinho claimed he would like one more attacking player that can play through the wings.
Reports now claim Martial has given his consent to a potential swap as he would be happy to move to Milan and test himself in Serie A.
United have been unwilling to let him leave which is the reason why a deal has stalled as both clubs failed to agree on a fee in negotiations.
Gazzetta dello Sport believes there is a general sense at Inter that United will cave into their demands and pay the transfer fee before the end of the window.
Perisic scored 11 goals and provided a further 11 assists last season as Inter finished a disappointing campaign, but Martial should not be allowed to leave, even if it is only a loan deal.