Crystal Palace are hopeful an improved offer potentially worth a club record £31.5m will persuade Liverpool to part with Christian Benteke as Alan Pardew seeks to revamp his squad further before the new Premier League campaign.

Last week an opening bid of £25m was rejected by Liverpool for the Belgium forward, who cost £32.5m when joining from Aston Villa a year ago. Palace’s new proposal is understood to be worth an initial £27m, with further fees linked to appearances, achievements and the club’s ability to qualify for Europe. Personal terms are not expected to prove problematic because the 25-year-old is keen to revive his career, although negotiations continue over the player’s image rights.

Benteke scored 10 goals in 42 appearances for Liverpool, joining initially under Brendan Rodgers but failing to convince Jürgen Klopp that he will be a key player under the German’s regime. The striker, whose involvement at Euro 2016 was limited to 10 minutes over two substitute appearances, has attracted interest from West Ham United this summer but is believed to be willing to move to Selhurst Park, with Palace having failed to sign his compatriot Michy Batshuayi. The latter has since joined Chelsea for £33.2m.

Benteke would join Andros Townsend, a £13m arrival from Newcastle United, and the France No2 goalkeeper, Steve Mandanda, who has been signed from Marseille for £1.4m, at Palace and should soon be followed by West Ham’s James Tomkins. The former England Under-21 international is expected to complete a £12m move across the capital, having been omitted from his club’s pre-season tour of the US and was due to have a medical on Monday.

There remains the possibility that Yannick Bolasie could depart Palace this summer. The DR Congo winger, such an integral part of the club’s emergence over the past few years, had been in talks over a new deal and it would take an offer in excess of £20m to persuade Palace to sell. West Ham have been mooted as potential suitors.