The Danish midfielder can leave on a free transfer when the season concludes, as he signed a short-term deal in January.
However, Frank believes that Eriksen's impressive return to the Premier League with the Bees may convince him to give it another season at the club.
Frank said at a press conference: "I would love to say 100 per cent, but I am convinced there is a good chance he can wear the Brentford shirt.
"I know I am optimistic but I also picked up the phone and said, "Hey do you want to come to Brentford?" No-one thought about that six months ago. I am convinced we will have a chance.
"The way I will see it for us is it is a win-win. He helped the team, he gave something to the fans they had never seen before at this level. We helped him back to his football life again.
"For Christian, it is a win-win. Either he signs with us and everyone is going to be happy and the fans will build a statue of him outside the stadium in two or three years' time, or he goes to a bigger level and fans will applaud him and we will all say, 'Thank you for this time, go forward'."
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