Ronny Deila stressed his desire to keep Fraser Forster at Celtic following the 4-0 victory over KR Reykjavik.
Executive vice-chairman Ed Woodward insists Manchester United are ready and willing to break the British transfer record.
Mike Phelan says Manchester United would have delivered a marquee signing had Sir Alex Ferguson's regime remained at Old Trafford.
Ferguson took the decision to slip into retirement at the end of the 2012/13 campaign, passing the managerial reins on to fellow Scot David Moyes.
With chief executive David Gill also vacating his post, it proved to be a summer of transition for the red half of Manchester.
Transfer plans were hindered as a result, with Marouane Fellaini the only new arrival despite several targets being chased.
Phelan, who left his assistant manager role alongside Ferguson, feels United missed a trick, with Moyes unable to wrap up the kind of deal that his predecessors had in the pipeline.
He told a Scandinavian United supporters' club magazine: "If Sir Alex and David Gill had still been the bosses, I won't name the player, but there would have been a star signing, one of the absolute best players in the world.
"It was something the boss talked about, and the owners and David Gill were also quite clear on doing it.
"There's very few of such players out there. I think it's clear to everybody who I'm talking about.
"We didn't see the need for a big clear-out of the squad, that's why Sir Alex and I had the one big signing in sight. One such star signing gives everybody a lift, we saw that with Robin van Persie."