The 30-year-old is weighing up his options amid interest from a host of teams across Europe including Tottenham and Manchester United.
Back in January, Brentford offered Eriksen a chance to resume his career on a six-month contract after the midfielder suffered a cardiac arrest while playing for Denmark at Euro 2020 last summer.
He surpassed all expectations in 11 appearances, scoring once and registering four assists.
Thomas Frank's side won seven of the 11 games in which Eriksen featured and sources claim Brentford were among the first clubs to offer him a deal for next season.
However, Spurs and United have also made contact with the player's representatives and sources claim there are also interested parties outside the Premier League -- a level of attention which has left Brentford fearing they are going to miss out on his signature.
Eriksen is thought to have enjoyed his time in west London and it is not impossible he could yet stay at Brentford but last month he expressed a desire to play in the Champions League again.