Mawson joined the newly promoted side from Swansea in a £15million deal in August.
However, Mawson is yet to feature for the club due to injury.
Mawson undertook an intensive recovery programme before returning to Fulham training.
Now, it sounds as if Mawson is on the brink of making his Fulham debut.
Jokanovic suggested that Sunday's Premier League clash with Burnley could be too soon, but that the Carabao Cup tie against Exeter could provide the perfect debut.
"Mawson has started working with us after a long period of being inactive on the field," Jokanovic said.
He had the last two days training with us, he is going to need the time for building fitness."
"Next week [we will] try to use him some minutes in the Carabao Cup, we still need to decide if we are going to try use him for 45 or 60 minutes."
"We are going to observe the situation but we believe he can start competing with us."