Rashford played with Zlatan at Man United where they won the League Cup and Europa League before he left in 2018.
The 39-year-old is likely to face his former side in the second leg of their Europa League clash with new club AC Milan on Thursday - with commentary of the match live on talkSPORT.
The Sweden international missed the first leg through injury - with the tie nicely poised at 1-1.
Fernandes has had an incredible impact at United since joining from Sporting Lisbon in January 2020.
He's scored 35 goals in just 65 games and has been the driving force behind their upturn in fortunes.
When asked if there were similarities between the pair, Rashford told talkSPORT: "Yeah you could say so. Mentally, they are both so strong and they want to win games.
"That's the atmosphere and the culture at this club, so we need to start doing it now; we need to start winning trophies and take steps in that direction.
"The game tomorrow is an opportunity for us to take one step forward."
The Europa League remains one of the few options United have of winning some silverware this season.
Rashford insists that their aim is to win the whole thing.
He added: "That's the aim when we unfortunately got kicked out of the Champions League, the focus was to win the Europa League.
"Anything less than that and I know the team, manager, staff aren't going to be happy with that. We're going to do our best to win this competition."
Marcus Rashford believes there are similarities between Zlatan Ibrahimovic and Bruno Fernandes in that both have that 'winning mentality'.