The midfielder made 43 league appearances for the Serie A club before heading to the Euro 2020 tournament with Denmark.
Eriksen’s football career was turned upside down when he suffered a cardiac arrest during their opening group stage match against Finland in June.
The Bees are thought to be in talks with Eriksen and have offered him a six-month deal with the option to extend for a further year.
The Premier League side are hopeful they have an advantage in their pursuit of the midfielder through their manager - and fellow Dane - Thomas Frank.
Why did Christian Eriksen leave Inter Milan?
Following Eriksen’s cardiac arrest at the Euros, the former Spurs star was fitted with an implantable cardioverter-defibrillator device - a decision described by team doctor Morten Boesen as ‘necessary due to rhythm disturbances’.
In October 2021, it was announced that Eriksen was not permitted to play in Italy due to the ICD.
Serie A rules prevent players from playing in competitive matches with a defibrillator and so his contract with Inter Milan was terminated.
No such regulations exist in the Premier League - and many other leagues - and so the 29-year-old has attracted interest from a number of clubs outside Italy.