No clause is written into Frimpong's deal with the club that could see him make a definite move across London in the summer but the midfielder is so far out on the fringes at Arsenal that Jol is quietly confident a suitable Fulham offer would be accepted.
But the Dutchman is keen to stress that he will wait until the season's ended before making any judgement on the player. Frimpong has only started once since moving in January and after some sublime performances from fellow loanee, Eyong Enoh, could be considered some way down the pecking order.
But one thing that is clearly on his side is his age.
"Frimpong is a young player and was a very good option for us," Jol said ahead of tomorrow's tie with the Gunners, for which the midfielder is ineligible.
"We needed midfield players and then one day before the transfer window closed I had the opportunity to get [Eyong] Enoh, who I knew of course.
"I'm happy Frimpong's here and he's played his part. When we took him everyone was very positive about him.
"He's a little warrior, but he's very young. I feel he's got a good future ahead of him."
Jol was coy, though, as to the possibility of making the move permanent.
"There have been no talks yet because the season isn't finished. Hopefully he will stay fit and I'm certain he will play a part for us, then afterwards we can make an assessment."
Frimpong, in his rare forays into the first team at Fulham, has looked assured and every bit as menacing as we expected but there is no doubt that Enoh has outclassed him. The Cameroonian has an extra six years of experience over Frimpong, who is 21, and it has shown in abundance.
But the likelihood of retaining Enoh is particularly slim while Frimpong would be open to a move. And, as Jol pointed out, the Arsenal man would bring some much needed youthful colour to an ageing midfield.
He won't get many opportunities to impress for the remainder of this campaign, Enoh will see to that, but if Jol likes what he sees on the training ground, then Frimpong could become a permanent member very quickly.
The youngster would add inevitable steel and guile to midfield, though his disciplinary record is perhaps an unwelcome side effect. Alongside somebody creative - a must-buy in the summer - Frimpong could flourish.
With what our manager has alluded to over recent weeks, this could well be a summer of upheaval and, if it starts with the purchase of Emmanuel Frimpong, I certainly won't be upset.