Celtic manager Brendan Rodgers admits the club "still has work to do in the market" but is "hopeful" the squad can be added to this week.
The Scottish champions have made six summer signings, but half of those have been on free transfers, and questions remain over whether the board have sufficiently backed the manager this window.
Celtic begin their Scottish Premiership title defence at home to St Mirren on Sunday - live on Sky Sports - and are closing in on a loan deal for Manchester City centre-back Jahmai Simpson-Pusey.
"We still have work to do in the market but I'm really excited," Rodgers told Sky Sports News.
"The focus is really on the players that are here, and they've been working very well and hopefully by the end of the month, we'll be a stronger squad for the end of the transfer window.
"We hope this week there might be some news on that (transfers), but I think coaches in the transfer market don't move at the same pace
"A coach always wants a player in immediately, but the transfer market doesn't always work like that.
"You want your team together as quick as you can so you can get some good work in, get the togetherness, get the spirit, get everything formed. But of course, we know that traditionally it can be a challenge.
"A coach will always want the players in. I think it's arithmetic; it's purely counting.
"We've lost players and we want to replace those players with quality. So it's not an opinion, it's where it's at. We've lost key players and we want to replace those as quick as we can in order to keep developing."
Are Celtic stronger or weaker than last season?
Celtic started the window quickly when they announced the return of academy graduate Kieran Tierney upon the expiry of his contract with Arsenal, but they are yet to replace some notable departures.
Winger Nicolas Kuhn left for Como earlier this month, and some supporters want more attacking options after talisman Kyogo Furuhashi left in January, while Jota is expected to miss a large spell of this campaign through injury.
"Listen, for me the focus is very much on what's here," added Rodgers, when asked if his squad is stronger or weaker.
"We know we have work to do and I'm hopeful that we can get that done by the end of the window.
"But in the meantime, as I said, the players have worked fantastically over the course of this pre-season.
"Some really good performances and [we've] grown and developed in our spirit, which is going to be really important for us."
Celtic v St Mirren - live on Sky Sports
Celtic will raise the league flag in front of the same team they lifted the Scottish Premiership trophy against in May, with the match against St Mirren live on Sky Sports on Sunday.
"Flag day represents an occasion that allows you to reflect a little on the season that has passed, in which we were champions and played very well," added Rodgers.
"But it is also a reminder of what lies ahead, a lot of hard work, and that hard work will start with St Mirren.
"Stephen (Robinson) has an excellent record at St Mirren over the last three seasons, guiding them into European football. He's a very good coach, so he'll have his team very well organised and up for the game.
"But for us, it's our first home game and we really want to go and start how we need to go on."
