The Red Devils are keen to strengthen their midfield ahead of the new season, with new manager Erik ten Hag linked with several reinforcements.
United's new boss is yet to make his first signing, but that could well be Eriksen given club chiefs were in attendance in Vienna for the UEFA Nations League clash.
Denmark won the match 2-1 away against Ralf Rangnick's Austria, with goals from Pierre-Emile Hojbjerg and Jens Stryger Larsen securing the three points.
A leaked document on social media, however, led to a surge of theories regarding the players involved in the match with many believing that United might have been taking a closer look at the Denmark international.
Eriksen, 30, is a free agent after his short-term deal with Brentford recently expired.
He has already proven he still has what it takes at the highest level during his time with the Bees, and can continue to make a huge impact in the English top-flight.
A move to Old Trafford could be on the agenda given he is available on a free, and he would help to address United's problems in midfield.
Juan Mata, a similar type of player, will leave the club at the end of the month.
It has also been confirmed Paul Pogba will depart for free when his contract expires, with a move back to Juventus being mooted.
Meanwhile, Eriksen is no stranger to Ten Hag, after he spent time training with former club Ajax before his move to Thomas Frank's Brentford.
The playmaker was reportedly said to be 'flattered' by United's interest previously, and will consider all of his offers ahead of the upcoming campaign.
He has also been linked with both former club Tottenham and their north London rivals Arsenal.
Spurs, West Ham and Borussia Dortmund also had scouts in attendance for the match, along with a host of other European sides.
It remains unclear as to whether Eriksen was the player United scouts were watching, but he will certainly have caught the eyes.