Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
The Reds have long been linked with the former Barcelona wide-man, who moved to Portugal last year.
His time with Sporting has not been hugely successful as he has been beset with a number of injuries and this season he has started just one game.
Now he is back on Liverpool's radar, together with a number of other Premier League clubs.
His agent Jorge Llagostera told Portuguese radio station Antena 1: "Yes. Liverpool and other Premier League clubs are monitoring the kid.
"But, formally, we still not have received an offer to negotiate with Sporting."
Any prospective deal could be hampered by the fact Barca have a buy-back option - but they would need to pay £9.6million to do that.