Rashford has impressed during his loan spell at FC Barcelona this season, but the Spanish champions have still not confirmed whether they will activate their option to sign him permanently for around 26 million pounds.
With the transfer window approaching, Stam believed a move involving AC Milan star Leao could suit all parties and give Manchester United a new attacking threat.
"Maybe a swap between Rafael Leao and Marcus Rashford could work," Stam told ComeOn. "Leao is a very good player and he has shown his potential at Milan. I think he is a player Manchester United should be looking at."
Stam also stressed that United must think beyond talent alone when targeting players this summer.
"You need to look not only at the quality of a player, but also the mentality and personality," he said. "The club needs players who fit the long-term project and who can help move the team forward."
Leao has continued to attract transfer interest after another strong campaign in Italy. The Portugal international has scored nine Serie A goals this season and has been used across several attacking positions by Milan.
Despite having a reported release clause worth 131 million pounds, the 26-year-old is believed to be available for a lower fee if Milan decide to reshape their squad this summer.
Rashford, meanwhile, has ended the season in excellent form. The England forward scored in Barcelona's title-winning victory over Real Madrid CF at the weekend, taking his tally to 14 goals in all competitions.
While Barcelona continue to weigh up a permanent move, Rashford's future remains one of the biggest talking points ahead of the transfer window, with Manchester United still facing a major decision over the forward.
