Eriksen has started courting interest from the big clubs again after impressing for the Bees on his return to football.
After being released by Inter Milan because of his heart issues, Eriksen joined the Premier League debutants in the January transfer window and has been instrumental in their bid against relegation.
Eriksen has so far scored one and provided two assists in eight appearances for Brentford.
Having signed a short-term contract with Brentford, Eriksen is set to become a free agent again in the summer, leading to links with the likes of former club Tottenham Hotspurs.
Speaking after Brentford's 3-0 defeat to Manchester United on Monday, Frank reiterated his desire to keep hold of his compatriot for a longer period.
When asked about keeping his compatriot, Frank told BBC Sport: "I am always positive. I always believe we have a very good chance.
"I know he is happy here, he is enjoying his football. It is a decision that will be taken at the end of the season."
He added on Sky Sports: "The key is he performs consistently at a high level ... It's no secret we would like to do everything we can to keep him."
Brentford are currently 14th on the Premier League table, eight points above the relegation zone.
