The 30-year-old footballer spent the second part of last season playing for Brentford, where he logged one goal over 11 games. He played a key role in Brentford finishing 13th on the Premier League table but turned down the opportunity to stay with the club.
Eriksen previously played for Inter Milan in Italian Serie A but the team terminated his contract in December 2021 following an incident in which he went into cardiac arrest during a European Championship match played for his native Denmark.
United has been busy over the last week, also signing 22-year-old left-back Tyrell Malacia from Feyenoord. Malacia has reportedly already finished his physical exam, but the club is waiting to announce the two new signings simultaneously.