New Celtic manager Ange Postecoglou admits there is an “urgency” over “a couple of positions” ahead of the Champions League qualifiers.
The 55-year-old Greek-Australian took charge of his first training session on Thursday with his side due to host Denmark’s Midtjylland on 20 July.
Postecoglou hopes “to make some announcements very soon” in terms of new signings.
But he says it is “a challenging time” for all clubs trying to sign players.
“Certainly, there’s an urgency in a couple of positions with this game coming up in a couple of weeks time,” he said at his first media conference at Celtic Park.
Norway centre-half Kristoffer Ajer was quoted in recent weeks as saying he wished to leave Celtic, while there is speculation about French striker Odsonne Edouard also wanting a move.
Postecoglou says he has yet to talk to either player but confirmed he has held discussions with striker Leigh Griffiths, who is out of contract at the end of June.
The 30-year-old told BBC Scotland this week that he hoped to agree a new contract within days, but Postecoglou suggested Griffiths would be given the same chance as all the other players to prove they can be part of his plans.
“I have had a good chat with Leigh,” he said. “He is in the same place as everyone else. We will continue those discussions and make that decision when I have all the information.”
Postecoglou, who had been managing Yokohama F Marinos in Japan’s top flight, was appointed shortly after Celtic’s discussions with former Bournemouth manager Eddie Howe broke down.
“I might have been fifth choice, I don’t know, it doesn’t really bother me,” he said. “What’s important to me is that I’ve been given the responsibility and opportunity and that fact shows people have faith in me. That’s all I need.”
Asked to respond to those who question his credentials for the job, Postecoglou pointed to his experience as Australia head coach, having previously won the domestic title with Brisbane Roar.
“I’ve coached at a World Cup and I’ve coached against some of the best teams in the world,” he said. “I look at it as another opportunity, an exciting challenge and an opportunity to work where I know people are so passionate about the game.”
Postecoglou admits he faces a “fairly extensive” rebuild of his squad and backroom team after Celtic’s failure to secure a 10th consecutive Scottish league title.
“In terms of management style, I am a builder and this is the process we are in at the moment,” he said. I’ve managed to navigate a career where I have merged good football with success.
“A team that’s exciting to watch, that scores goals, doesn’t fear anyone and doesn’t take any backwards steps. The reason I do that is because it brings success wherever I’ve been.”
Postecoglou indicated he will decide the future of his backroom team, including John Kennedy, who had been caretaker manager, in the coming weeks and confirmed he has granted the players who have returned from Scotland duty at the Euros time off.
“The priority for us right now is to make sure that, when our first Champions League game comes around, we are as ready as possible,” he added.
‘Postecoglou gives relaxed impressions’ – analysis
BBC Scotland sports news correspondent Chris McLaughlin at Celtic Park
The new manager seemed relaxed during his first encounter with the media. What shone through was his message that he can say what he wants but he knows he’ll be judged by his actions. He also mentioned his style of play several times and the fact that he has experience rebuilding squads.
New chief executive Dominic McKay was keen to push the work the club is doing to get fans back inside Celtic Park. He also said he’s working very closely with the Scottish Government – something he did well in his role at Scottish Rugby.