Frimpong is on loan at Fulham for the rest of the season and his Arsenal contract is due to expire in the summer.
Jol said that while it would be "expensive" to sign Frimpong permanently, he would be interested in another loan deal should the player stay at Arsenal.
"If there was an opportunity to take him on loan, I would probably do that," the Evening Standard quotes Jol as saying. "It is quite a nice position to be in, to get a loan player you do not have to pay a transfer fee. It is a good way of doing things because it would be quite expensive to take him [permanently].
"I was impressed with him from the start. He is the type of player you would like as a manager because he is versatile and he can play as well because he is an Arsenal player."
Frimpong has made just one appearance for Fulham since joining at the end of January.