The Scottish champions remain frustrated in their ongoing pursuit of Hibs midfielder John McGinn after having three bids for the player turned down so far.
As Celtic attempt to claim a place in the lucrative group stage of the Champions League for a third successive year under Rodgers, the manager says achieving significant improvement on the standards set in the past two years requires a level of investment which is out of his control.
Celtic have broken their own transfer record this summer, paying £9 million for the permanent signing of French striker Odsonne Edouard, who spent last season on loan from Paris Saint-Germain. That has been balanced to a large degree by the sale of midfielder Stuart Armstrong to Southampton for £7m.
“I’m not sure,” was Rodgers’ blunt response when asked if he expected his squad to ultimately be stronger when the window closes at the end of next month.
“I’ll work with the players who are here, the players that we have, and then obviously whatever the club can do, they will do. But my focus is on the players who are here in the building and ready to work.
“The club works in a specific way. You don’t need to be a rocket scientist to know that if you are going to improve drastically from where this group is at and where it has got to over the last couple of years, that in order to make the improvements that people want to make, it costs money. But that is out of my control.”
There is now fresh speculation over the club’s Belgian World Cup defender Dedryck Boyata who is entering the final year of his contract and has been linked with Fulham, Lazio and Lyon in the past few weeks.
Celtic’s lack of depth in the central defensive area is an issue once more ahead of tonight’s Champions League second qualifying round, first leg meeting with Rosenborg in Glasgow, when they will be without the suspended Jozo Simunovic.
With Boyata yet to return from holiday after the World Cup, it leaves the relatively inexperienced duo of Kristoffer Ajer and Jack Hendry as Celtic’s only recognised central defenders.
“The problem is that if you are going to bring in a top, top centre-half then that is going to cost you big money,” added Rodgers. “That is out of my control. If not, then you have to do what the club has always done. You bring in players who fit the model of the club and you develop them and improve them and then probably eventually they move on. Somewhere along the line you’ll need that level of experience to come in and try and support and then you hope that can work out for you.
“Dedryck has done well in the last 18 months for us and did well at the World Cup, so naturally there’s going to be interest in him.
“We don’t want to lose him, he’s a very valuable player for us, but at some point if he doesn’t sign his contract, then of course he’ll go into his last year and then naturally what happens there is he either goes onto another club or stays.
“That’ll be up to him in the end but at this point in time he’s very important for us to help us achieve our goals early on in the season.
“I’m not sure at this stage there’s an offer (for him) that would make us even think about it because of the stage of the season we’re at. We’re playing very important games that can set us up for the season. We need our best players available for that and he is clearly one of them.”
With a third round qualifier against Greek champions AEK Athens up for grabs, Celtic suffered another blow when striker Moussa Dembele was ruled out of both legs of the Rosenborg tie by the hamstring injury he picked up against Armenian side Alashkert last week.
Edouard, however, has recovered from a knee problem which threatened his involvement and is likely to play just in front of Tom Rogic who is back in the squad after his World Cup exertions for Australia.
“Part of the challenge is to find a way,” said Rodgers. “We played Rosenborg last year with no strikers but got through. We’ll put out a team that will be really competitive and hopefully get an advantage to take to Norway next week.”