The 26-year-old South African frontman currently plays for Mamelodi Sundowns but is keen to try his luck in Europe again after spells with Strasbourg and Reims.
Glyn Binkin said: "I can confirm that Mphela has an offer for a trial with Glasgow Celtic. I passed the letter of invitation on to Sundowns in the last 24 hours.
"Maccabi's (Haifa) best offer was Â£1.3m but there are other clubs, like Dynamo and Celtic, who could afford as much as Â£1.5m.
"Clubs like that want to be able to see the player before signing, though. Katlego's an unknown quantity in Europe. He played there before but didn't quite make it the first time, so clubs want him to come on trial first."
Mphela has already seen potential moves to Partizan Belgrade and Dynamo Kiev fall through.