Liverpool have taken their summer spending to L80m – and could reach the L100m mark in the coming days – after agreeing a L20m fee with Southampton for Dejan Lovren.

The Croatia international’s signature has been a priority for Brendan Rodgers all summer as the Liverpool manager seeks to address his team’s defensive shortcomings and a deal has finally been agreed for the centre-half to become the third player to transfer from St Mary’s Stadium to Anfield since the end of last season. Lovren is expected to undergo a medical on Merseyside on Saturday.

Southampton had rejected a previous offer of L16m for the World Cup defender, who they signed from Lyon for L8m 12 months ago, but with Lovren informing new manager Ronald Koeman he wished to leave for Liverpool, and the Dutchman reluctant to keep unhappy players at his club, the improved offer has enabled Rodgers to make his fifth summer signing. Lovren will be Liverpool’s first defensive acquisition with a left back, potentially Chelsea’s Ryan Bertrand or Sevilla’s Alberto Moreno, also required.

Liverpool’s lavish outlay is not purely from the proceeds of Luis Suarez’s L75m sale to Barcelona and the Premier League runners-up are close to adding L8m Loic Rémy and fellow striker Divock Origi, a L9.8m signing from Lille, to their ranks.

France international Rémy, who spent last season on loan at Newcastle United, underwent a medical earlier this week in Boston where Liverpool had been in pre-season training. Belgium international Origi had his medical in the United States on Friday and both deals are now subject to administration details.

Liverpool took advantage of a release clause in Rémy’s contract with Queens Park Rangers following the departure of Suarez to Spain. The 27-year-old scored 14 goals for Newcastle last season, making a major impression before his and the team’s form nose-dived after the sale of Yohan Cabaye, and 27 goals in 68 appearances for Marseille before joining QPR in 2013.

Liverpool have already signed Rickie Lambert and Adam Lallana from Southampton, Emre Can from Bayer Leverkusen and Benfica’s Lazar Markovic ahead of next season’s return to the Champions League. They could also be joined at Anfield by defender Javier Manquillo on a season-long loan from Atletico Madrid.