ESPN reports the American could return to the club where he spent time as a youth player in their academy.
Lennon, 19, was the subject of an offer from the USA side but the Reds turned it down after it fell short of their valuation of the player.
But Real Salt Lake are now looking to bring the attacker back to the States in a loan deal.
Lennon moved to Anfield in the summer of 2015 after impressing on a trial at the club.
The Arizona native is under contract at the Merseyside club until 2018 and has progressed from the Under-18s to the Under-23s.
But Jurgen Klopp has yet to give him his senior debut but is hopeful a loan move can provide him some experience of regular football.