The 30-year-old had an implantable cardioverter defibrillator device fitted after suffering a cardiac arrest while representing Denmark at Euro 2020, which saw him leave Inter Milan.
Eriksen made the move to Brentford in January, and he impressed for the Bees in the second half of the 2021-22 campaign, scoring once and providing four assists in 11 Premier League appearances.
The playmaker's contract with Thomas Frank's side is due to expire at the end of June, and he is widely expected to leave the club in search of pastures new.
Manchester United are believed to have offered the attacker a contract, with new Red Devils head coach Erik ten Hag said to be keen to bring him to Old Trafford for the 2022-23 campaign.
Tottenham have also been credited with an interest in their former player, but according to Football Insider, the North London outfit have now 'pulled the plug' on a potential deal.
The report claims that Spurs had talks with Eriksen over a return to the club but 'discussions have not progressed', with the capital team now out of the race for his signature.
The Dane previously represented Tottenham between 2013 and 2020, scoring 69 goals and registering 90 assists in 305 appearances in all competitions.
When questioned on his plans earlier this month, Eriksen insisted that he would not be rushing a decision on his future.
"No (rush the decision), and they know that too," Bold.dk quotes Eriksen as saying. "There are many criteria and many different things inside such a decision. Sometimes it goes fast in football, other times a little slower. You are not in control of it yourself. I have to make the best decision and not rush anything through.
"My phone stays on, but I also know my agent well enough to know that he only calls if there's something exciting."
Meanwhile, Eriksen said that he has "different offers and options" this summer and insisted that moving to a team competing in the Champions League is not a priority for next term.
He told Viaplay: "I have different offers and options, which we are considering, and then we make a decision. I would love to play Champions League football again. I know how much fun it is, but it isn't essential for me."
Tottenham, who finished fourth in the Premier League last season, have already been busy in the summer market, signing Ivan Perisic and Fraser Forster on free transfers, while Yves Bissouma has arrived from Brighton & Hove Albion.
Spurs will open their 2022-23 Premier League campaign at home to Southampton on August 6 before travelling to Chelsea in their second match of the season.