The Addicks boss is due to meet the player on Friday with the intention of trying to keep him at the Valley for the club's Championship campaign.
The 22-year-old has been in talks with Rangers over a move north with Steven Gerrard hopeful he is in place before the club's pre-season training camp.
With the player out of contract at the end of June, Aribo would only cost £250,000 due to age cross-border rules.
Bowyer will make a case that it would be better for him to stay put for one more season.
Speaking to South London Press, he said:"I've told him to come and see me, tell me his options and we can have a chat.
"He needs to stay and do a year in the Championship with us - so that he learns more. Then it might be a case of him leaving next season.
"It would be a huge thing if he stayed and kept learning because the big moves will come later on, if he does it right.
"Joe is a great lad, so we are going to have to wait and see what he says."
Aribo was interesting Celtic and a host of English clubs but it is beleived he has his mind set on a move to Rangers.
They will travel to Rugby Park on Sunday, 4 August.