The 31-year-old has scored 17 goals in 72 appearances for Liverpool since joining from Atlético Madrid on a free transfer in January 2010.
However, the Argentina international has struggled to secure a regular place in the Reds’ first-team, despite scoring an impressive 10 goals – including two hat-tricks – in the 2010-11 campaign.
The former Atlético captain had been linked with a return to the club where he started his career – Newell’s Old Boys – but new Liverpool boss Rodgers is keen to keep Rodríguez at Anfield.
“I have known about Maxi for a long time. He will understand 120 per cent about the way I want us to play,” Rodgers told Liverpool’s website.
“But sometimes there are issues that surround that – that’s what I am speaking to him about now. He doesn’t speak the language, it has been difficult for his family.
“If a player like him wanted to leave, it would not be because of the club. Sometimes it is just personal issues. I have had a couple of really good conversations with him. I know his thoughts and how he is thinking. It was a difficult season for him. He probably felt that he should have played more.
“We will hopefully see where he is at over the next couple of weeks and find a solution for him.
“But he would be a very good player for our squad.”
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