The Red Devils are thought to be on the brink of completing a deal to sign the Brazil international in the summer transfer window.
Fred would strengthen Jose Mourinho’s options in the middle of the park after Michael Carrick ended his playing career at the end of the 2017-18 Premier League season.
Belgium international Marouane Fellaini is set to become a free agent at the end of the campaign, while Ander Herrera has struggled to convince under Jose Mourinho.
Manchester United finished in second place in the Premier League table last term ahead of Tottenham Hotspur, Liverpool FC and Chelsea FC.
However, the Red Devils ended up 19 points adrift of Premier League champions Manchester City to highlight the widening gap between the two clubs.
Former Tottenham defender Dawson doesn’t believe Manchester United will catch Manchester City with the addition of Fred.
“I just look at Manchester United and they’re going to need to sign more than just Fred to close the gap on Manchester City,” Dawson told talkSPORT.
“I just think they are just so far ahead of any other team, I really do.
“They just keep going and going and if you’ve got a bottomless pit like they have, how do you get closer?
“If someone spends £100m, they’ll spend £200m, £200m then they’ll spend £400m, that is what Manchester City do.
“Look at the staff, I know one of the fitness coaches there and anything that’s needed it’s not like ‘oh we’ve maybe got to see the budget’, it just gets bought. So they have the best.
“Manchester United are in the same (bracket), but not quite the same in the way they go out and spend. You look at Chelsea and Roman (Abramovich) doing the same, Liverpool, Spurs.”
Manchester United haven’t won the Premier League title since 2013 when Sir Alex Ferguson won his 13th and final top-flight crown.
The Red Devils lost 1-0 to Chelsea FC in the FA Cup final at Wembley last month.
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