The Liverpool manager Roy Hodgson is hoping to bring the Manchester City left-back Wayne Bridge to the club after completing the signing of Chelsea's Joe Cole.

Cole's deal was finalised yesterday after the 28-year-old England international passed his medical. He had already agreed personal terms with the Anfield club on a four-year deal worth £90,000 a week following his release from Chelsea last month.

Liverpool hope Bridge will be the next big-name signing and believe City could be convinced to sell for as a little as £6m, although the fee is more likely to be around £8m. Hodgson needs a left-back after allowing Argentina international Emiliano Insua to move to Fiorentina for £5m.

Bridge, who will turn 30 next month, is likely to fall down the pecking order at Eastlands once the long-awaited £17m signing of the Lazio left-back Alexander Koralov has been completed. City manager Roberto Mancini is believed to want Koralov to replace Bridge in the starting XI next season, leaving the former Southampton and Chelsea defender facing a season on the bench.

Liverpool hope Bridge will appreciate being offered a change of scene following the turmoil he experienced last season. He brought his 36-cap international career to a close in February following revelations that the then England captain John Terry had an affair with his former girlfriend Vanessa Perroncel. At the time Bridge described his position in Fabio Capello's England squad as "untenable and potentially divisive".

Cole yesterday described his decision to turn down offers from Arsenal and Tottenham Hotspur to plump for Liverpool as "a no-brainer because they are the biggest club in the country".

Cole, 28, denied suggestions he chose Liverpool simply because they were the only club to match his wage demands, and instead said he thought purely of footballing matters. Cole said the memory of the noise from the Kop in 2005 when Chelsea lost to Liverpool in the second leg of the Champions League semi-final was a major factor in his decision.

Cole said: "I tried to take everything out of the equation, take the financial and location side out and just thought in football terms. I thought about the semi-final of the Champions League in 2005 when I ran on to the field and the hairs on the back of my neck stood up. I was thinking about playing in that atmosphere every week and that swung it for me."

Cole won plenty of trophies during his seven years at Chelsea, including three Premier League titles, but admitted to growing frustrated at not playing regularly enough.

"One of the factors in my decision was coming to a club where I'd be able to string 90 minutes together," he said. "Your body needs to get used to the sharpness of doing it week in, week out. I've had a difficult couple of years but I'm coming here as an experienced player who is still fresh and excited about it.

"I think players can play for other clubs but with Liverpool you have to live and breathe it. It's that kind of a place. I know what they [Liverpool fans] want and know they want a team to be proud of. I'll go out there every day and live and breathe the club and give my all. I just want to get myself fit. I'm a bit behind in my training work but I want to get fit and help the team to achieve something. I want to be part of a team that's capable of doing great things."

Cole's signing was followed by confirmation from captain Steven Gerrard that he is not looking to move away this summer. Hodgson, however, predicted yesterday that he is still some way from having a squad that is strong enough to compete for the Premier League title.

The manager said: "Last season was a very disappointing season for the club in every respect, culminating in a popular manager leaving. You don't change doom and gloom or disenchantment with a signing or two."

Liverpool yesterday completed the signing of 18-year-old Rangers defender Danny Wilson. They will pay £2m up front with a further £3m dependent on appearances and add-ons.

Last night the Hodgson era opened with a goalless draw against Grasshoppers Zurich with Cole watching a youthful Liverpool line-up from the sidelines.