Ange Postecoglou is optimistic Celtic will announce some new signings "in the next few days" as he insisted it was not his responsibility to convince wanted members of his squad to stay.
New signing Osaze Urhoghide made his debut on Saturday as Celtic ran out 2-1 winners against Charlton in the club's second pre-season friendly win of their training camp in Wales.
The futures of Odsonne Edouard, who came on in the second half of the match in Newport, and Kristoffer Ajer remain uncertain, with one year remaining on the pair's contracts at Celtic Park.
Speaking after the game, Postecoglou told reporters: "We are trying to get some players in and hopefully get some deals done.
"We need some players to come in because we lost a fair few from last year. It is not an easy process at the moment, but we are pushing hard and hopefully we will get some in the next few days."
Postecoglou is building his new side towards the first leg of their Champions League second qualifying round tie against Midtjylland on July 20.
Asked if Celtic had received any bids for their players, Postecoglou said: "To be honest, I am not as focused on outgoings as I am on incoming. Incoming is where my pure focus is at the moment. I can't control who leaves, what I can control and push for is to bring people in."
The Greek-born Australian added: "I'm focused on a couple of key areas - working on the players we have here and trying to get players in.
"I guess it will come down to whether players want to be a part of this or not. Some may have already made their minds up, others will make their mind up as they go along.
"I am not here to plead our case at the moment. That is not the business I am in. If people want to be a part of it, I am happy to include them."
Postecoglou insisted that bringing in another forward is not a priority, despite Leigh Griffiths leaving the training camp amid an ongoing investigation by Police Scotland over alleged improper online behaviour.
"We need players in a number of positions, it's not just one," he said. "Even looking at those who have gone from last season, purely on numbers, we need players."
One player who appears to have a chance of a revival under Postecoglou at Celtic is midfielder Olivier Ntcham.
The French midfielder, who spent the second half of last season on loan at Marseille, saw a proposed move to AEK Athens collapse and made his first appearance of pre-season against Charlton.
"I had chats with him and he said he wanted to come back and make an impression this year," the former Australia boss said.
"I take that at face value. He has been good at training.
"He is lacking a bit of match touch and fitness but he is part of the squad and hopefully he can make an impact this year."