De Jong has played down the idea of heading to Old Trafford in the summer transfer window and insists he is ‘very happy’ at the Catalan club.
The Netherlands international was one of Erik ten Hag’s top targets last year and United had even agreed a €85 million (£72m) fee with Barcelona.
But the 25-year-old midfielder stood firm and refused to leave the club – and despite De Jong making it clear that his preference is to remain at Barcelona – United are understood to have retained their interest in signing the player.
Cole, though, has urged United to give up as he told King Casino Bonus: ‘I look at it from the outside, is Frenkie de Jong the midfield player that could do a job for Manchester United? No he’s not.
‘De Jong is a very good player and there is no disputing that, but if you look at last season’s transfer saga and you have to wonder why would Manchester United want to put themselves in that position again?
‘They need to go for players who actually want to come to the club like Casemiro did.
‘Going in for De Jong again makes them look desperate, this is Manchester United football club we’re talking about here, if you don’t want to play for them then move on to your next option.
‘It’s not like Manchester United is a non-league football club, the answer to the move should be yes or no, not a maybe.
‘I’m looking at the two games Barcelona played against Manchester United and you can see they were not the better team.
‘But if they win La Liga, De Jong will be thinking what’s the point in him leaving Barcelona, especially if they fix their financial problems.
‘I just want Manchester United to know they can go out there and attract any top player.
‘It’s not about money, these top players that are available will all be fought for and paid a decent wage anyway, so that makes no difference anymore.
‘Players will look at their chances to win the Premier League, FA Cup or League Cup and the Champions League.
‘Everyone wants to win their domestic league and Champions League.
‘Look at Real Madrid’s form in La Liga compared to when they play in the Champions League, it’s like they play two separate teams but it’s just a case of mentality.’