Tottenham, Newcastle and Manchester United are among the clubs linked with Eriksen.
But Frank added: “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.”
Eriksen resumed his playing career with Brentford after collapsing while playing for Denmark at Euro 2020 last summer.
He has been fitted with an implanted cardioverter-defibrillator (ICD), a type of pacemaker, after suffering cardiac arrest.
Eriksen has been arguably Brentford’s stand-out player and on the winning side in six of the eight games he has played, with the others a goalless draw against Tottenham and then Monday’s loss at Old Trafford.
Eriksen also scored in the 4-1 win at Chelsea on 2 April.
Asked how Brentford are trying to convince him to stay, Frank said: “Very simple, I speak to him. We are presenting our plans and discussing it back and forth.”
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