Assistant manager Johan Mjallby wants Celtic to bring in up to four more new faces before the new season kicks off.
Celtic have made approaches for Sol Campbell, Joe Ledley and Jamie Bullard, while George Boateng is at the club's training complex in Lennoxtown.
"It's important we get winners and guys like Sol Campbell and George Boateng are winners," said Mjallby.
"In a perfect world, we would like to get three or four good players in before the start of the season."
Manager Neil Lennon has already signed two full-backs this summer in South Korea international Cha Du-Ri and Charlie Mulgrew.
And joining 35-year-old Dutch midfielder Boateng at Celtic's training complex this week is Montenegran attacking midfielder Slovan Stjepanovic, 22.
"George Boateng has only been here a day and there has been a lot of running," explained Mjallby. "Hopefully he can stay on for a couple of days and we can have a look at him playing football as well.
"Slaven has been training for a few days with us. For all the players the first few days has been just running and not too much football.
When I first came here, I saw that we had a lot of good ball players in the side but we lacked a wee bit of steel
"We have started to get the balls out now and it's a better chance for us to have a look at them."
Celtic are also pursuing the Mexican World Cup winger Pablo Barerra, who is also interesting clubs in England.
Speaking for the first time since his appointment as Lennon's assistant last week, Mjallby added that he hoped Welsh international Ledley would move to Glasgow.
The 23-year-old midfielder who is out of contract at Cardiff City has been a visitor to Lennoxtown but is also wanted by Stoke.
The Swede, who helped Lennon see out of the tail end of last season on an interim basis, expressed a desire to see Aiden McGeady remain at the club.
However, he did admit that a large fee may be too tempting to turn down for the the Republic of Ireland midfielder.
A tough-tackling centre-half in his playing days at AIK Stockholm, Celtic and Levante, Mjallby wants to see more bite from his players next term.
"When I first came here, I saw that we had a lot of good ball players in the side but we lacked a wee bit of steel," he said.
"We lacked mental strength and you could see that away from home, where we dropped too many points and conceded too many silly goals.
"If you want to be successful, you need to be strong and win the battle before you start playing the good football."
Since the end of a disappointing last campaign without silverware, Celtic have released Lee Naylor, Zheng Zhi and Koki Mizuno and lost loan signings Robbie Keane, Landry N'Guemo, Edson Braafheid and Diomansy Kamara.
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