However, he stressed: “I see us doing more to get us set up for hopefully what will be a really exciting season.”
Tierney departed Celtic for Arsenal in a £25m transfer six years ago and the Scotland international has returned Glasgow as a free agent.
“Sometimes top players like that might come back later on in their career, but we’re getting Kieran at 27 years of age,” Rodgers said.
“I was with him during the summer, so I know first hand as well how excited he is to be here and I’m looking forward to seeing this new version of Kieran, having had the experience in the Premier League and playing at a top club like Arsenal.
“He’ll come back here with greater maturity both as a person, as a professional and tactically and now we can really get the benefits of that.”
Of Sweden cap Nygren, Rodgers added: “He’s a leader on the pitch and he produces on the pitch in terms of his goals he scores, what he creates and he’s got real good physicality.
“I’m really looking forward to seeing him adapt to how we play.”
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