Eriksen, 30, is available to sign on a free transfer as his Brentford contract expires on June 30.
The Denmark international signed a short-term deal with Thomas Frank’s side in January and made an immediate impression, helping the club to secure an impressive 13th-place finish.
Frenkie de Jong is believed to be the club’s top midfield priority, but talks are moving slowly. but Eriksen could be a good replacement, and much cheaper too.
Eriksen, speaking to Viaplay, said:
“I have different offers and options, which we are considering, and then we make a decision.
“I would love to play Champions League football again. I know how much fun it is, but it isn’t essential for me.”
Brentford have been very interested in extending the midfielder’s stay in west London, but last month Eriksen said he was considering multiple options from numerous different clubs.
Former Ajax manager Erik ten Hag has taken over the reins at Old Trafford after joining the club on an initial three-year deal.
Eriksen trained with Ajax’s reserves before joining Brentford in January in order to get back up to speed following his cardiac arrest at the delayed Euro 2020. He played for Ajax between 2010 and 2013.
Tottenham Hotspur also said to be interested in Eriksen according to a new report, and a return to his old club would also reunite him with Antonio Conte, his old manager at Inter Milan.