However, reports have surfaced that Celtic decided against exercising their right to sign the centre forward.
The KwaZulu-Natal target man had been training with Celtic, but was released on Friday.
“Yes, the coaches did not want to sign him,” Konco told Goal.
Celtic have also confirmed that they will continue to search for new additions to bolster their squad.
“We are looking to bring in other players,” Konco concluded.
Goal did attempt to get a comment from the player’s agent Miguel Paiva. However, he was unavailable at the time of publishing.
Mthembu joined the Amakhosi in 2014, but has struggled for first team football ever since.