The Red Devils were linked with a potential move to sign the Denmark international in the summer transfer window but a deal failed to come to fruition.
Manchester United midfielder Paul Pogba continues to be linked with a move to La Liga giants Real Madrid and Serie A champions Juventus following a difficult 2017-18 campaign.
Eriksen was touted as a potential replacement for the World Cup winner but the Premier League’s transfer window came and went without the Danish star completing a move.
The Tottenham star has established himself as one of the Premier League’s best creative midfielders over the past three or four seasons.
Eriksen has scored 66 times in 277 games in all competitions since his move to Tottenham in an £11m deal from Dutch side Ajax in 2010.
Former Manchester United midfielder Scholes believes the Red Devils missed a trick after Ole Gunnar Solskjaer failed to recruit Eriksen for his overhaul at Old Trafford.
“I was quite excited when Christian Eriksen got mentioned [as a Man United target],” Scholes told Robbie Savage’s Premier League Breakfast, as quoted by the Daily Mirror.
“He could have made a big difference to United in the way De Bruyne plays for City, creating chances and scoring goals.
“But they haven’t got that and they have some good players so the target is top four and I think they will make it.”
Manchester United were 4-0 winners against Chelsea FC in their opening Premier League fixture at Old Trafford on Sunday evening.
The Red Devils haven’t won the Premier League title since 2013 and have only managed to finish in the top four twice in the past six seasons.
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