Scott Brown, the Celtic captain, has insisted that he would trust Brendan Rodgers “with his life” as he maintained that he believes the Parkhead side will improve again this term whether there are further new arrivals or not.

Celtic have made goalkeeper Scott Bain and Odsonne Edouard permanent members of the squad after signing them on long-term contracts this summer, with the outlay for Edouard a club record fee believed to be almost £9m.

Read more: John Hartson: Celtic can bury Rangers with the right signings this summer

I suspect that as the game goes on and Rosenborg leave more and more space as they look for openings, that Celtic should be able to exploit the gaps that they will leave in their wake.

That has been offset by the sale of Stuart Armstrong to Southampton for £7m while defender Erik Sviatchenko headed back to FC Midtyjlland for £1m.

"I put a lot of trust in the manager and he's produced a lot to be fair,” said Brown. “I trust him with my life. The way he's doing things at Celtic he's improving us in every single department. so yes I have a lot of trust in him.

Celtic have had three bids for Hibernian and Scotland midfielder John McGinn knocked back by the Easter Road side this summer and there has been some frustration on the part of supporters at the lack of further new additions to the squad.

There has been a hint of discord over the lack of signings with Rodgers clipped at times when asked about the ongoing nature of his enquiries for players.

Read more: John Hartson: Celtic can bury Rangers with the right signings this summer

Celtic will head to Trondheim this afternoon in preparation for the second leg of the UEFA second round Champions League qualifier against Rosenborg with a threadbare defence following injury and suspension issues.

It seems to have become something of a perennial issue for the club to be exposed at this point in this season, as they look to negotiate a difficult qualification process to the group stages of Europe's premier competition.

Dedryck Boyata and Mikael Lustig were given additional time off after their involvement at the FIFA World Cup while Jozo Simunovic is suspended and Marvin Compper has an adductor injury.

Brown, though, was vocal in his belief that whatever squad is there when the transfer window closes at the end of August is one which Rodgers can continue to get the best out of.

"We've got a great squad in that dressing room," he said. "We all stick together on and off the park. We are a very tight knitted group and if the manager wants to bring someone in then we have all faith in him to bring someone in. But if he doesn't believe we need anyone then I think we can do the business with the squad we have got.

Read more: John Hartson: Celtic can bury Rangers with the right signings this summer

"We have got Ryan Christie and Scott Allan too, we have Mikey Johnston and Calvin Miller coming through too. We have got two young ones coming through and two experienced ones who have played in the Premiership who have come back into the squad."

And Brown has revealed that he came back from his summer holiday in better shape than when he went off on it.

“The games seem to help me, I get stronger and stronger as they go on," he said. "Last year I felt great all the way through the season.

“My fitness levels are not a problem,” he said. “It’s just a question of avoiding injuries and making sure I keep ticking over every week.

“I looked after my body well in the summer and came back in better nick than I was at the end of the year.

Meanwhile, Celtic have decided not to appeal the additional suspension that UEFA’s disciplinary body gave to Simunovic on Friday. The Croatian defender will miss tomorrow night’s second leg, second round qualifier against Rosenborg as he serves the second game of the ban for his dismissal in the first round against Alashkert.

Celtic opted against an appeal after learning UEFA’s full reasoning behind the suspension. Any appeal would have endangered his availability for the potential third round tie against AEK Athens.