Manager Jose Mourinho is eager to bring in more attacking reinforcements before the start of the new Premier League season, with only Fred and Diogo Dalot having arrived at Old Trafford so far this summer.
United are also considering reviving their interest in Inter Milan forward Perisic following his performances at the World Cup, but The Independent reports that they could make a move for Perisic's Croatia teammate Rebic.
The 24-year-old is significantly younger than United's two other targets and would also be much cheaper, with Chelsea demanding up to £70m for Willian and Inter holding out for £80m for Perisic.
Rebic only joined Frankfurt on a permanent deal earlier this summer, with the German outfit triggering an option for just €2m (£1.7m) to sign him from Fiorentina.
Willian is still understood to be Mourinho's priority, but Rebic is now regarded as a contingency plan for United should they miss out on their top target.