Everton have agreed a fee of £27m for Besiktas forward Cenk Tosun, according to Sky sources.
And the 26-year-old Tosun will travel to Liverpool on Thursday to begin his medical ahead of the planned move.
We understand Everton officials were in Turkey over the weekend to discuss the deal and that the talks continued in London on Wednesday night.
“Whether that is enough, only time will tell.”
Tosun has been capped 25 times by Turkey and has been in fine form this season, scoring four goals in the Champions League to help Besiktas reach the last-16 for the first time.
And Allardyce is hoping to make the former Gaziantepspor man his first signing since taking charge at Goodison Park in November.
Everton are keen to add to their options up front, last season’s top scorer Romelu Lukaku having been sold to Manchester United last summer.