The 29-year-old hasn't played since he suffered a cardiac arrest in Denmark's opening group game against Finland at Euro 2020 last June.
Eriksen has been fitted with an implantable cardioverter defibrillator (ICD) to monitor his heart rhythm.
But the device meant the Danish playmaker was unable to extend his stay at Inter Milan where he helped the Italian club to their first league title in 11 years under Antonio Conte's stewardship.
He made a surprising return to the Premier League by joining Brentford on Deadline Day.
Bees head coach Thomas Frank spoke ahead of their clash against Crystal Palace and insisted their is no timeframe on his debut right now.
He said: "I think he's fine, he's training well and he looks like the quality player we know he is.
"It's a joy watching him play football - so natural for him - so that's fantastic to see, but he will not be available for the team tomorrow. That would always be too early after just one week.
"We will have a friendly game on Monday where he will play minutes and that's the right way to do it."
The former Tottenham midfielder reunites with Frank who managed him Denmark at youth level.
And the Bees manager believes the Danish international remains in good spirits and will stay at the club for the reminder of this season.
Frank said: "I must say he's bubbling. We are having him seven months after the incident so he missed badly being part of the group, being part of a club and hopefully we can add new chapters to the Brentford story.
"He loves to be with the boys, being on the grass, playing football.
"He's one of those where he needs to touch a ball all the time, so when the drill is done, and I start talking and as soon as we start again, he just needs to touch a ball or something like that.
"He's just enjoying it, he's bubbling and just wants to play football."