United reportedly had a bid of around £40 million ($51m) for the 21-year-old rejected by Palace, who are said to be holding out for £60m ($76m).
The right-back was named Player of the Year at Selhurst Park after an excellent first full season in the first-team, in which he made 39 appearances in all competitions.
Despite his performances, ex-Palace star Salako believes a switch to the Red Devils would be a big risk for Wan-Bissaka and urged him to learn from team-mate Wilfried Zaha, who left for Old Trafford at the age of 20 only to return to Selhurst Park before long.
"You want young talent. He's got the world at his feet. But my only concern is that we had Wilfried Zaha leave at a young age and he didn't cope," he told Love Sport Radio.
"He wasn't mature enough and didn't really settle in at Man United. He ended up coming back and has had the best spell of his career since he came back. He's obviously another one linked with moving away but I'm just a bit concerned with Aaron.
"It's been his first full season and it's been absolutely magnificent. He couldn't have been lying in bed and dreamt of a better debut season. He probably needs more games.
"I would compare him to Nathaniel Clyne who came through the system at Palace and was tremendous. He played 120-odd games and then went to Southampton, Liverpool, played for England and everything seemed to fall into place for him because he had that maturity. He knew his job and he was confident in himself and his game."
He added: "It's too early for Aaron. He needs another season. I'm not surprised United have come in because they could probably get him cheaper and they think they need to do something now.
"You remember with [Theo] Walcott and those types of players who came through at Southampton - even [Gareth] Bale or [Alex] Oxlade-Chamblerlain - they came early and it took them years to find their feet. I don't know why teams don't buy them and then leave them with their club and loan them back for a season or two, just to get that maturity. Then they've got the player at the right price.
"I think United are trying to get players on the cheap. That's one of the things I'm frustrated with at Palace. There is a DNA, lots of local players that have come through at your Brentfords and in the lower leagues. We used to pick up Ian Wright from [Sunday League side] Ten-em-Bee, or from local sides like Sutton or Carshalton or Croydon.
"You've got to take a chance on those players lower down the leagues for £5m or £6m and they can turn into £40m players. That's where the value is. You look at [Joe] Gomez who went for something like £5m from Charlton to Liverpool. What value that is! Those are the kind of deals that Manchester United are now looking to pick up."
Zaha has also been linked with a move away from Palace after recording 10 goals and five assists in the Premier League in 2018-19. The 26-year-old has four years left on his contract, having signed an extension in August, but Salako believes it is a good time for him to go.
"It sounds as though he wants to [move to a top-six club] from what I've heard coming out," Salako added.
"He feels this is the time. He's certainly ready. I think he's had his best season so far. He's matured, he's added so much to his game. In all honesty I think it's down to him.
"He's got the physicality, he's got the ability and now he's just got to add that little bit of temperament. He's getting frustrated at Palace because he is targeted because he is such a key man. If he played in a better side, there would be other better players that would attract more attention and take that pressure off him a little bit.
"If he's got the desire to go and play Champions League football and he wants to play at a big club, I don't think any Palace fan can deny him that. He's been magnificent and you would wish him all the best from the bottom of the heart. He is a player that would excite and compliment and work well in any team."