The Premier League giants have been eyeing a move for the Croatian for some time, but they have so far been unsuccessful in persuading Inter to sell.
Numerous reports claimed earlier in the summer that United tabled a £44m offer for the 28-year-old, but it appears that the Italian club are holding out for more.
According to the Manchester Evening News, the Red Devils are likely to make another move for Perisic this week, but Inter want Anthony Martial included in the deal.
It is believed that the North-West outfit are unwilling to part with the French forward, who had to fight for his place in Jose Mourinho's team last season.
The Portuguese coach is reportedly keen to bring in two more signings before the transfer window shuts at the end of the month.