The Uruguayan spent two-and-a-half years at Anfield before leaving for Barcelona in 2014.
He has since left and joined Atletico Madrid where he has continued to produce.
Barnes told Goal: "If they could get Luis on a free transfer that'd be ideal but it'll come down to whether Luis says he wants to play every week or he'll be happy to move across and be part of the squad.
"But, because of his age, I don't think he could expect to be playing every week.
"The tricky things with these type of transfers is that you have to be pretty certain that the player in question isn't going to upset things.
"Liverpool needs to recreate their team spirit and togetherness and, in order to do so, the players need to be happy with where they are and level of play. If Luis can do this, then great - get him on board."