The Italian has struggled to adapt to life at Anfield - scoring only two goals in all competitions since his close-season arrival from Milan - and has been linked with an early exit.
Inter are reported to be among his suitors, with Roberto Mancini having coached the striker previously at San Siro as well as at Manchester City.
However, with Liverpool eager to improve their Premier League form while also challenging in the League Cup, FA Cup and UEFA Europa League, Rodgers wants to keep his squad together.
"It is not something I have even thought about," he said of Balotelli's potential exit.
"We have had a lot of games this season in a lot of competitions. At this moment in time, it is key for me to keep the squad together."
With Balotelli misfiring since his return to England, Liverpool have often looked to Raheem Sterling to play in a more advanced role this term.
Sterling struck the winner in Friday's 1-0 victory over Burnley and Rodgers hailed the England international's pace.
"Raheem and anyone with that type of pace will always stretch teams and always make defenders think," he added.
"He's a different type - he's not your natural number nine - but for me it's more about the position rather than the player for the team to function well.
"That pace in the team is very important for us."
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