The Cottagers refused Rangers' initial bid of around £3million but Walter Smith has upped his bid in an attempt to secure the permanent signature of the 23-year-old.

Smith had hoped to wrap up a deal before Thursday night's Champions League qualifying round transfer deadline but Fulham's apparent reluctance to accept anything below their £4million valuation means that the Gers must face Kaunas next week with their current squad.

Rangers were known to be looking at other targets in case a deal for Davis can not be agreed however the sale of Sulley Muntari to Inter Milan means Portsmouth can afford to reject any offer the Glasgow club submit for Pedro Mendes, who Harry Redknapp is keen to keep hold of.

Sunderland midfielder Dickson Etuhu is also on Smith's radar but his priority remains a deal for Davis, who made 25 appearances for Rangers after joining on loan on the final day of the January transfer window.