Everton have agreed a £25m deal with Besiktas to sign the Turkey striker Cenk Tosun, with the 26-year-old ready to sign a four-and-a-half year contract when the transfer window reopens on 1 January.

Despite an unbeaten run of seven matches that has pulled them clear of the relegation battle, Everton have scored only 24 league goals this season and have been searching for a striker to replace Romelu Lukaku. Another attempt to sign Arsenal’s Olivier Giroud was rebuffed earlier this month, with Arsène Wenger keen for the France international to remain at the Emirates. This led to a formal approach for Tosun.

Allardyce has tracked the former Eintracht Frankfurt and Gaziantepspor player for some time and recommended him to Crystal Palace, who had a bid rejected in the summer. A brilliant season for Besiktas in which Tosun has scored 13 times – including four in the Champions League as his club reached the knockout stages – has seen his stock rise considerably.

Everton’s offer of £15m was rejected before an agreement was struck on Tuesday, with Besiktas set to receive around £20m up front and another £5m in performance-related clauses. It is understood Tosun’s father and agent accompanied him to the club’s training ground on Wednesday to discuss personal terms and complete his medical.

Born in Germany, Tosun joined Eintracht Frankfurt’s youth system in 1997 but made only one appearance for the first team before moving to Gaziantepspor in 2011, where he spent three seasons. He joined Besiktas in 2014 and has scored 41 goals in 96 matches.

Despite making two appearances for Germany’s Under-21 side, Tosun opted to play for Turkey at senior level and has eight goals from his 24 caps.