There were fears that the 30-year-old's playing career was over after his horrifying cardiac arrest at Euro 2020, which led to him being fitted with an ICD.
After being forced to call it quits on his time with Inter Milan, Eriksen built up his fitness with Erik ten Hag's Ajax side before returning to the Premier League with Brentford on a short-term contract.
Eriksen quickly became a regular for the Bees with one goal and four assists in 11 top-flight outings, but his deal with Thomas Frank's side will expire at the end of the month.
The former Tottenham Hotspur man is believed to have caught the attention of several top sides following his remarkable comeback and impressive start to life back with the Danish national team.
Eriksen played the full 90 minutes of his side's 2-1 win over world champions France last week and was also named in the first XI for the trip to Austria on Monday night.
Ahead of the contest in League A Group 1, FA intermediary Paul O'Keefe revealed a long list of clubs with scouts in attendance, including Man United amid links with a transfer for the playmaker.
The likes of Tottenham, West Ham United and Borussia Dortmund also sent representatives to watch Denmark scrape a 2-1 win, where Eriksen claimed the assist for Jens Stryger Larsen's deciding goal.
A recent report claimed that Man United have now entered the race to sign Eriksen this summer, although Brentford manager Frank is not giving up hope of a permanent contract.
"I know I am optimistic but I also picked up the phone and said, 'Hey, do you want to come to Brentford?," Frank told reporters last month.
"No-one thought about that six months ago. I would love to say 100%, but I am convinced there is a good chance he can wear the Brentford shirt.
"Either he signs with us and everyone is going to be happy and the fans will build a statue of him outside the stadium in two or three years' time, or he goes to a bigger level and fans will applaud him and we will all say, 'Thank you for this time, go forward."
Tottenham are also believed to be interested in bringing Eriksen back to North London after he scored 69 goals and set up 90 more in 305 appearances for the club between 2013 and 2020.
The former Ajax man has now registered 52 goals and 71 assists from 237 Premier League appearances, but he is yet to come to a final decision over his future.
Man United have already lost two playmakers in Jesse Lingard and Juan Mata on free transfers, while Lee Grant, Edinson Cavani, Nemanja Matic and Paul Pogba have followed suit.