Daniel Agger has banished any uncertainty over his Liverpool future by signing a contract that ties him to the club until 2016. The influential Denmark defender was the subject of a £20m bid from Manchester City in the summer, an offer that Liverpool rejected as they held out for £27m for the 27-year-old.

Neither City nor Barcelona, who were also linked with the centre-half, matched Liverpool's valuation and it was only after the transfer window closed that talks commenced on extending a contract that had less than two years remaining.

Agger had made it clear that he wished to remain on Merseyside and, although the length of the deal has not been announced, it is understood to be an improved four-year contract.

The defender, signed for £6m from Brondby in 2006, said: "It means everything to me. This is where I want to be and I'm happy the club want me. I am really happy right now. I've never wanted to go anywhere else. I feel I am a part of this club and I want to be a part of this club in the future. I like the way it is going right now with the style we're playing, and hopefully the results will come soon as well."

Agger is playing with a small fracture of his knee cap, suffered in the home defeat by Manchester United, and was rested from the Europa League defeat against Udinese on Thursday. He is expected to return for Sunday's Premier League game at home to Stoke City.

Ian Ayre, Liverpool's managing director, said: "Daniel always made it clear he wanted to stay at Liverpool and we're delighted that he's committed his future to the club. We brought in some very exciting players this summer – some of whom chose Liverpool over clubs in the Champions League.

"But it's equally important to retain your most important players and the fact that Daniel has now followed Luis Suárez, Martin Skrtel and Jonjo Shelvey in signing a new contract is testament to the fact that the players believe in what we're trying to achieve here under Brendan Rodgers."