The 33-year-old striker scored six goals in 24 appearances for the Reds after moving to Anfield for the second time in his career last summer.
The Wales international has been linked with a return to Cardiff this summer as Brendan Rodgers looks to leave trim his Liverpool squad.
“I had a really good meeting with Craig before I moved up here,” said Rodgers. “He is a big Liverpool supporter but I also understand his thinking.
“He is 33 and has travelled around the country all his life, so there are compassionate reasons.
“We will look at it but we will wish him all the best and move forward.”
Meanwhile, Rodgers reiterated his desire to keep hold of Denmark captain Daniel Agger amid reported interest from Premier League champions Manchester City.
The Eastlands outfit had a £10m bid for Agger rejected by the Reds, although Rodgers hinted the club would be willing to sell the centre-half if they received a big offer.
“Daniel is a top player and you do not want to lose your best players,” added Rodgers. “He has been here seven years. He loves the club and its supporters.
“But every player has his price and we will see where it goes.”
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