The four-times-capped Ghana international arrived at McDiarmid Park for a training stint organised by former boss Craig Levein in late October.
However, the subsequent signing of former Dundee United, Lech Poznan, and Leeds United star Barry Douglas has put paid to Korsah’s hopes of a deal in Perth.
Valakari stated that Douglas is likely to be the last free agent signing for the club until January.
"Right now, we have Barry (Douglas) and Andre (Raymond) in the left-back position, so we are well stocked," he told The Courier. "It wouldn't make sense to add another player. Dennis will find another team."
He also indicated that St Johnstone would only consider signing additional players in case of an emergency situation. "It would be tough to find more free agents at this point, and we’d only look if we faced a critical need in one position," he added.
Korsah left Accra Hearts of Oak at the beginning of the 2024/25 season after completing his contract.
Korsah joined Accra Hearts of Oak from Ebusah Dwarfs in 2022.
He helped the Phobians win the FA Cup and President Cups.
What is next for the defender?
Free agent Dennis Korsah will be looking for a new club following the Scottish Club opting out on him. He is likely to return to the Ghana Premier League to continue with his football journey as he eyes another club.