The Catalans' current number one Victor Valdes revealed last week that he would not renew his contract, which expires in 2014, as he wishes to broaden his experiences.
Valdes' announcement means Barcelona are on the hunt for a replacement, with the Spanish side likely to sell their current stopper this coming summer instead of allowing him to leave for free a year later.
And it would seem Reina would be a willing replacement should he receive a call from the Nou Camp according to his father.
"I am absolutely convinced that Pepe would be more than delighted to return to his Barcelona, where they made him into an upstanding man from the time he arrived at the age of 12 until he left," Miguel Reina said.
"I say it publicly, I would be delighted to see Pepe back at Barca, of course I would," added the former Barca and Atletico Madrid keeper.
Reina made his debut for Barcelona at the age of 18 and made a total of 30 appearances having come through the youth ranks, before leaving to join La Liga rivals Villarreal and eventually moving to Liverpool in 2005.
Liverpool will be in a strong position should Barcelona make a move, with Reina having signed a six-year contract in 2010.
Liverpool defender Jamie Carragher admits he is open-minded about his future at the club as the clock ticks down on his contract.
The veteran centre-back turns 35 next Monday and his existing deal only runs until June.
Asked whether he could play on beyond this season, the former England international said: "That's up to the manager and the club will make decisions like that."
Meanwhile, Brendan Rodgers is confident of completing the £8million signing of Inter Milan midfielder Phillipe Coutinho before Liverpool's FA Cup tie with Oldham.
Rodgers is in advanced negotiations with Inter over a deal to sign the Brazil international.