Michael Dawson is ready and willing to lead Hull next season in the Sky Bet Championship.
Dani Alves still feels not "fully respected" at Barcelona and has hinted he will leave after the season.
Reina, who is on a season-long loan at Serie A side Napoli, has been strongly linked with a move to the Primera Division giants at the end of the campaign to replace the outgoing Victor Valdes.
Barca's current number one announced in May that he would leave the Nou Camp at the end of this season and Reina, who began his career at Barca before making a name for himself at Villarreal and later Liverpool, would relish a return.
However, the 31-year-old knows the Catalan club will have many targets and has refused to look past helping Napoli this season.
He told El Mundo Deportivo: "I would love to return to Barcelona.
"To play at Barca is a privilege.
"But I imagine that my name is on a list with others.
"Barca is a top club and Victor Valdes' departure will have alerted other candidates so a return will be very difficult.
"Right now I'm not thinking about it.
"I was fortunate to play there once and I consider myself privileged to have done that.
"The important thing is that I continue to do well at Napoli."
Reina has three years remaining on his contract with Liverpool but is unlikely to return to play at Anfield with Reds manager Brendan Rodgers preferring Simon Mignolet.