Barcelona are set to be on the hunt for a new striker in the summer with Luis Suarez now 32 and Lionel Messi turning the same age in June.
Rashford has a contract with Manchester United until 2020 but talks have begun over a renewal amid speculation of a transfer.
While Aubameyang joined Arsenal last January and has been prolific goalscorer with 28 goals for the club.
And Kluivert, who scored 90 goals for the Spanish side, feels both players fit the profile of a Barcelona forward.
“I like Marcus Rashford, a lot,” Kluivert told Sport365. “It will be really difficult to get him over. But he is a good player.
“I don’t see a lot of players who can play in Barcelona. [Arsenal’s Pierre-Emerick] Aubameyang, perhaps he can play.
“There is not a lot. Maybe some players who can play in La Liga, young players. But for me, I think the best one is Marcus Rashford.
“He has got the skills, the attitude, he’s quick, he’s fast, he can score goals.
“He is not always in the first XI at Manchester United and maybe he wants to change club. So why not?”
Rashford’s performance since Ole Gunnar Solskjaer‘s arrival in December have dramatically improved.
Against Leicester, he scored his sixth goal in eight league games and has now scored more goals in all competitions since his debut (42) than any other United player.
But Jamie Carragher feels Rashford can be United’s long-term first-choice striker.
He told Sky Sports: “The form he’s in at the moment, if he continues that, they won’t need to buy anyone else or bring Romelu Lukaku back into the side. He can be United’s main man.
“I was at this ground to see England against Switzerland and we debated that night whether Rashford could ever be that man.
“I was doubtful of that but what’s happened under the interim manager – we talk about an audition for the manager but Rashford can make himself United’s centre-forward, show he can be the man to take you to a title or a Champions League.”