Coutinho and Jurgen Klopp have both recently played down such speculation but Tite has told Sport that it is logical that Barcelona would want Coutinho to link up with compatriot Neymar.
He seems convinced that the former Inter ace has the attributes to flourish in that deeper role though, and while Barca will welcome the favourable assessment of the Brazil coach who indirectly may influence Coutinho's thinking, it's not what Liverpool want to hear at all.
Coutinho has been directly involved in nine goals in his last nine Premier League games, turning on the style to help Liverpool into the Champions League places.
Tite, however, believes that a move could work for Coutinho as he would slot seamlessly into Barcelona's current system. "There was one goal [for Brazil against Paraguay] they were brilliant for, Neymar on the left, Coutinho coming in to the middle".
"Just to be clear, I'm talking hypothetically..." There's Sergio and the two creatives, what in Italy they call "mezzalas", that are Rakitic and Iniesta, the two thinkers of the team.
Liverpool's job though is to convince him we can compete with the very best during next season's Champions League, giving him no reason to seek pastures new.
"In Liverpool, Coutinho plays for the left, but the important thing is that he performs the same function for the national team". "Look, if I was Klopp I would fight to make sure I kept hold of him".
Asked about the possibility of putting Neymar and Coutinho together at club level, Tite said: "Yes". Coutinho, like many South Americans, have an affinity with Barcelona as many of their childhood heroes played there.
"We need to create alternatives. We will only see this when we do it".
Celine Dion Performs 'Titanic' Hit "My Heart"
Celine Dion gave a heartwrenching performance of her hit song My Heart Will Go On at this year's Billboard Music Awards . Even co-host Vanessa Hudgens got teary and her co-host Ludacris called for another round of applause.