O'Shea has questioned what role Eriksen would have if he joined the club.
“When a good player becomes available, they'll figure out a way to get him in if they can, and if the manager wants him. With Christian Eriksen, they would have had discussions about him," O'Shea told Paddy Power.
“Thankfully, he's got back to full fitness, and he showed his quality at Brentford last season. There's lots of boxes to be ticked in terms of what he can bring to the team but is he the necessary fit for this team at this time?
"Manchester United have to weigh up those options. Eriksen is a quality player, no one is denying that. But is he the right fit for what Manchester United needs at the moment? That's up to the manager and the recruitment team.
“There are other players at Ajax who Ten Hag should know very well and you'd hope that if there were certain individuals he thought could settle into the Premier League and Manchester United quickly, then hopefully they can get that over the line.
“I'm sure that behind the scenes, they'll be discussing that and hopefully those things can happen quite quickly."