The Premier League club announced the signing of the Denmark midfielder on Monday, seven months after he suffered a cardiac arrest at last year’s European Championship.
Frank, whose side play Everton in the fourth round of the FA Cup on Saturday, said the 29-year-old would train with his new team-mates for the first time next Monday.
“Christian has a solid physical foundation and has been doing all sorts of tests,” Frank said.
“He has been running a lot, training a lot, so he has done quite a lot over the last few months so his foundation is fine, but another thing is to get up to match speed.
“It is hard to say when he is available. I will know a lot more after Monday.”
Eriksen was released by Inter Milan in December as Italian medical regulations do not allow players fitted with cardioverter defibrillators to feature in Serie A.
Quizzed on whether it could be months before Eriksen makes his debut for Brentford, Frank admitted: “I hope weeks, a few weeks, but I don’t know. I am much more clever when I have seen him train.”
Frank labelled former Tottenham star Eriksen as potentially Brentford’s “greatest signing” and said his return to the pitch would be an emotional moment.
“We got it over the line and that was fantastic,” said the Danish manager, who is self-isolating after testing positive for coronavirus.
“The story behind it, I think it will be an unbelievable day the day Christian steps on the pitch,” Frank said.
“You guys have seen him performing as one of the best in the Premier League and what happened to him in June was crazy and a shock for us. The day he returns it will be emotional.”