Suarez previously spent three-and-half years with the Reds, scoring 83 goals in 133 appearances, before joining Barcelona in the summer of 2014.
The 34-year-old Uruguayan remains a fan favorite at Anfield but is now scoring goals for the Rojiblancos, who are locked in a battle for the La Liga title with Barcelona and Real Madrid.
Liverpool have uncharacteristically struggled for goals at times this season, with the likes of Roberto Firmino and Sadio Mane, enduring droughts in front of goal at crucial times of the campaign.
Jurgen Klopp’s men face a fight to secure Champions League football next season and Barnes is adamant getting the experienced frontman on board could be ideal for Liverpool’s attack.
Barnes, speaking in association with BonusCodeBets, 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.
"As a player, I think he's always given 100 per cent, and he's a decent enough character in terms of trying all the time without being disruptive. So, yeah, that wouldn't be a bad move for Liverpool.
"And I’m sure the fans would absolutely love to get Luis back and I do wonder if they may kick off if they feel that he isn’t getting enough airtime!"
