The Catalan club learned last week that Victor Valdes will not renew his contract, which expires in 2014, and in the days since have been linked with a number of keepers, including Manchester United's David De Gea, Chelsea's Thibaut Courtois and Reina.
The Liverpool keeper, 30, started his career at Camp Nou after coming through the youth ranks with Valdes but left for Villarreal in 2002 as his team-mate became the club's number one.
Now his father, who also represented Barca as a goalkeeper, says Liverpool's number one is ready to return to his first club.
Reina senior told laxarxa.com the Liverpool star "would be more than delighted to return to Barcelona."
He added: "I believe that Pepe has demonstrated enough the quality of keeper he is.
"Today I think he would rise to the occasion at Barcelona - and what's more he would be the ideal keeper for Barcelona, without any doubt."