The former Liverpool defender has backed Chelsea to finish second in the league table next season after winning the title during the 2016-17 campaign.
Tottenham Hotspur will also drop down a place from second to third in 2017-18, while United will break into the top four next season, according to Nicol.
The former Scotland international has also explained why Liverpool will not finish in the Champions League places next season, and has not mentioned Arsenal at all among the clubs who can challenge for the top four.
"I think going forward there is not a person who can argue they do not have quality, not just in the starting XI but coming off the bench as well, so for me it was all about defensively for City, and they have shown in the transfer window that they recognise that,” Nicol told ESPN FC about City.
“No, because, one, they haven't made any move whatsoever (in the summer transfer window)," said Nicol about Tottenham when asked why they won’t finish second next season.
"They've been so consistent over the last couple of seasons and deservedly finished second, but there’s no reason to think they can take that another step forward.
“And also, they are playing at Wembley. It's just not the same as being at home, that will cost them points during the season, which is why I think they will drop down from second last year to third this year.”
"Liverpool haven't really done anything so far to really shake themselves up in the transfer market,” said Nicol about Liverpool.
“Mohamed Salah is a good signing, but it just solidifies the quality they have in the front three more than anything else, but that's it. I think they need to do more.”
City have been quite busy in the summer transfer window so far and have made a number of signings, including that of right-back Kyle Walker from Tottenham.
Tottenham have yet to sign a new player so far this summer, but the North London outfit have a strong and stable team and the fans should be confident of yet another successful season.
Arsenal failed to end up in the top four of the Premier League last season for the first time in 20 years, and it seems that Nicol does not rate them much.
The Gunners could find it tough to claim a Champions League place yet again, especially with the competition they are going to face from the likes of Manchester United and Liverpool.