Coloccini signed a new a four-year contract in March after joining Newcastle in 2008 after four seasons at Deportivo La Coruna.
The Argentine informed the Magpies of his desire to return to South America earlier this month, with Alan Pardew vowing to keep the centre-half.
But Osvaldo Coloccini, currently a youth coach at San Lorenzo, says his son is desperate to quit and wants his future resolved as quickly as possible.
“Fabricio is very anxious, he wants a resolution,” he explained.
“I think that it’s the moment for him to return to San Lorenzo. We want him to come back.
“In the last few hours, Newcastle have bought a defender but that means nothing because they were looking for an option in that position anyway.
“At Newcastle they are telling him to wait until May but the thing is that I don’t know if San Lorenzo are going to be able to wait until then.”
San Lorenzo manager Bernardo Romeo confirmed the club are looking to sign a centre-half.
“We need a central defender. We are waiting,” Romeo added.
“Let’s have faith in that the transfer will be done, otherwise we will have to go out and look for another central defender.”