The 21-year-old is a fast-rising talent from South America whose recent performances have seen him compared to Paris Saint-Germain star Angel Di Maria.
Everton reportedly have competition from Atletico Madrid, but Martinez has a Spanish passport so can move without a work permit.
Arsenal are also understood to have been watching Martinez, who scored a stunning goal against Penarol last month.
His record in Uruguayan football shows he is not prolific, with just one goal in 26 league appearances for Liverpool this year.
Sheffield United could have leading scorer Leon Clarke back for their home game against Nottingham Forest.
St Johnstone midfielder Murray Davidson is determined to use their derby exploits as a springboard to rid them of inconsistency.
Lincoln will once again be without skipper Luke Waterfall for Saturday's League Two derby clash with Grimsby.
Leeds boss Paul Heckingbottom is expected to choose from an unchanged squad for the home game against Sheffield Wednesday.
Derek Fazackerley will take the Oxford helm on the 56th day of his caretaker stint in Saturday's match against Peterborough.