With both players entering the final six months of their respective contracts in England, Koeman is rumoured to be tracking them as targets.
However, despite indicating his continued interest in both players, the Dutch boss claimed a move in the current window is unlikely.
“My position is known: we lack people, but the economic situation of the club is an influence,” as per reports from the Daily Mirror.
“I think we all think the same. If no one arrives, I will accept it and we continue on the same, but if we want more from the team we must sign players
“We have concluded that if he (Garcia) is a player whose contract is ending, we must wait.
“If we moved now we would have to pay the transfer fee plus the player’s salary (in each case).”
Barcelona are expected to continue to push ahead in talks with City centre back Garcia, with the Spanish international firm in his intention to return to Catalonia.
Wijnaldum’s situation remains less clear, with Liverpool expected to make a renewed effort to keep him at Anfield with an improved contract offer.
Koeman long standing interest in Lyon striker Memphis Depay also appears to have cooled, despite the former Manchester United forward being in an identical contract situation.