The forward is expected to leave Manchester United this summer after falling out of favour at Old Trafford and has admitted that he would relish playing on the same team as Barca's 17-year-old phenomenon.
In an interview with the Spanish YouTube channel xBuyer, Rashford said when asked if he would like to play wth Yamal: "Yeah, for sure, Everybody in the world wants to play with the best. Hopefully ... We'll see."
Yamal has established himself as one of the top players in world football despite his tender age and Rashford is amazed by the star's ability.
The striker - who made his debut for United aged 18 - said: "[It is] difficult to put into words what he is doing. He is not supposed to be doing that at 16, 17 [years of age]."
Rashford spent the second half of last season on loan at Aston Villa but hinted that he would prefer a move abroad this summer.
The England striker said: "Spain is nice, and it’s not too far from home."
Barca's sporting director Deco revealed last month that the La Liga champions were interested in signing both Rashford and Liverpool's Luis Diaz to bolster their attack.
He said: "We like Luis (Diaz), we like (Marcus) Rashford, and we like other players.
"When we go to the market, there are names that we know and that could improve the team."
However, Deco added that Barca's priority this summer was tying down the club's current stars to long-term contracts.
The former Portugal international said: "Our big priority is to strengthen what we have at home with the renewals of Pedri, Gavi, (Ronald) Araujo, Raphinha, (Jules) Kounde.
"Then, if the team can be improved. From what we've seen this season, we need a player with a different profile to what we have to help the strikers."