The Denmark international is believed to be free to leave Old Trafford before the market closes, with a recent report claiming that he could be available for as little as £5m.
The 32-year-old enjoyed an impressive 2022-23 campaign at Man United after arriving on a free transfer, scoring twice and registering 10 assists in 44 appearances in all competitions.
However, the midfielder found it difficult to show his best form last season, only managing one goal and three assists in 28 appearances, and he is yet to represent the club in 2024-25.
Eriksen was an unused substitute against Manchester City in the Community Shield on August 10, and he has also stayed on the bench for his side's two league games with Fulham and Brighton & Hove Albion this season.
Ajax 'weighing up' late move for Eriksen
According to the Daily Mail, Ajax are considering making a move for Eriksen before the transfer window closes.
The midfielder spent the latter stages of his youth career with the Amsterdam giants before progressing to first-team level in 2010, and his form in the Netherlands earned him a move to Tottenham Hotspur.
Eriksen scored 32 goals and registered 65 assists in 163 appearances for Ajax in all competitions, winning three Eredivisie titles and the Dutch Cup in the process.
Due to Man United's apparent desire to sell, Ajax could potentially negotiate the £5m asking price down, especially as Eriksen only has a contract at Man United until next summer.
Which other Man United players could leave before the transfer deadline?
Scott McTominay is on the verge of leaving Man United for Napoli, with the Scotland international's switch to the Italian giants set to be confirmed in the near future.
Jadon Sancho also continues to be linked with an exit; both Juventus and Chelsea are said to be keen on the Englishman, with a departure in the final stages of the transfer window expected to occur.
Victor Lindelof is another to be linked with a transfer, and Lazio are said to be weighing up a late move for the Sweden international, who has dropped down the pecking order at Old Trafford.
However, a deal at this stage could be difficult, so it is likely that Lindelof will see out the final year of his contract with the Red Devils before potentially leaving on a free transfer in 2025.
Away from transfers, Man United are currently preparing for Sunday's Premier League clash against Liverpool, and they have been hit with an injury blow ahead of that contest.