The pair have both made positive impressions at Hull, after arriving on long-term loan moves a the start of the season.
Bruce and Arsene Wenger have a very good relationship, and the former Manchester United player intends to call the Frenchman to see if he is able to sign either of the youngsters in the summer.
“Hopefully he [Wenger] thinks it’s a good home,” Bruce said. “We try and look after them and a year on loan at somewhere like Hull will do them the world of good.
“They have both had terrific years with us and I will be on the phone very, very quickly to see if I can make it permanent. I wouldn’t mind that at all.”
Hayden and Akpom have both played frequently for Hull this season, as Bruce’s side go for promotion.
Hayden, a 20-year-old central midfielder, has made six starts and eight substitute appearances in the Championship so far this campaign.
Akpom, meanwhile, has played 31 times and managed to score seven goals.
He has been one of the Tigers’ main goalscoring threats, with Abel Hernandez the only player at the KC Stadium to have scored more often.
Hull are currently top of the Championship, with their next match coming against Ipswich Town later this evening.