Liverpool sign goalkeeper Adam Bogdan

Liverpool have made their third signing of the summer with Bolton goalkeeper Adam Bogdan, another free agent, agreeing terms.

The 27-year-old Hungary international’s contract with Wanderers, for whom he made more than 100 Premier League appearances, expires at the end of the month and he will officially join the Reds on July 1.

Bogdan’s arrival follows that of Manchester City midfielder James Milner and Burnley striker Danny Ings, also both out of contract.

Liverpool are still trying to agree a suitable fee with the Clarets, who are entitled to compensation because Ings is under the age of 24.

An initial bid of £4million has been rejected with Burnley understood to be looking for a figure closer to £10million for the England Under-21 international.

However, Liverpool have a bigger issue to deal with currently after turning down a £30million offer for Raheem Sterling from Manchester City.

The bid, understood to be £25million up front with £5million of add-ons, was flatly rejected by the Merseysiders who value the 20-year-old in excess of £50million.

Sterling has 24 months left on his current deal and despite him turning down a £100,000-a-week offer in January and his agent Aidy Ward later claiming the player would not even sign for “£900,000-a-week” – comments which prompted Liverpool to cancel a scheduled meeting to reopen talks which were put on hold earlier in the year – the club believe they remain in a strong negotiating position.

Liverpool’s rejection is unlikely to deter City, whose chairman Khaldoon Al Mubarak on Wednesday promised “high-quality” signings this summer, or any of the other interested parties.

Manchester United were first to make their interest known, however, Chelsea and Arsenal – offering a return to Sterling’s home city – have also been linked while new Real Madrid manager and former Reds boss Rafael Benitez, who brought Sterling to Anfield when he was a 15-year-old at QPR, has also expressed his admiration for the forward.