The 30-year-old has been in superb form since joining the Bees back in the January transfer window.
It has led to his fairytale return for the Danish international team, following his cardiac arrest during the European Championship last year.
Now it has been reported by the Daily Star that the Red Devils have shown an interest in signing Eriksen this summer.
The club just this week have confirmed the long-awaited news that Ajax boss Erik ten Hag will be their permanent manager at the end of the season.
There is expected to be a big turn-around in players this summer, with Ten Hag expected to bring in some new faces to improve a faltering United squad.
It’s said that he has placed Eriksen on his transfer wishlist and believes he would be a perfect signing to launch his revolution at the Premier League giants.
Ten Hag got the chance to see Eriksen up close when the player spent time training with his Ajax outfit at the turn of the year as he continued his recovery from his cardiac arrest.
United’s next manager was believed to be hugely impressed by the former Tottenham midfielder’s quality – as were the rest of the players.
The Dutch club had considered re-signing the player who left them for Tottenham in 2013, though there were fears about his ability to perform at the highest level again due to his medical condition.
He has made seven appearances since his return to the Premier League and has helped push Brentford away from the relegation zone and now sit 11th – 12 points clear of the bottom three.
United are not the only club who have been linked with Eriksen, as Antonio Conte is reportedly interested in bringing him back to Tottenham.
The Italian worked with Eriksen during his time in charge at Inter Milan.
Eriksen only signed a short-term contract with Brentford so will be available for free in the summer if he decides to move on.