Podolski has scored 15 goals this season as his home club, to which he returned in 2009 after a hapless three-year spell at Bayern Munich, battle to avoid the drop.
He has been widely linked with a move to the Premier League next season.
"Lukas is a Cologne player at the moment and will be one until the end of the season," Solbakken told reporters during the team's training session. "Then we will have to see what happens.
"His decision is important for us but also for him. We have to respect that."
Cologne have so far failed in their efforts to extend the winger's contract with Podolski, who said he would take a decision in the off-season.
The Germany international has previously been linked with a move to Arsenal.
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