But Portuguese Football Federation president Pedro Proenca, who was appointed last year, is an admirer of Mane and keen to convince him to play for Portugal.
England Under-21 manager Lee Carsley is also taking a firm interest.
Mane, who moved to England aged eight, may initially be called for Portugal U21s but could also train with the seniors, with Martinez keen to fast-track him into his squad after the World Cup.
No decision on Mane’s international future has been made, sources have told BBC Sport, with Mane keen to focus on his club form.
He joined Wolves from Rochdale in February 2024 and made his debut under Vitor Pereira in a 2-0 defeat by Brighton in May.
This season Mane has been one of the few bright spots in Wolves’ wretched campaign after making a first-team breakthrough under Rob Edwards.
Mane has scored twice in 20 games – he became the club’s youngest Premier League goalscorer – but Wolves are bottom of the Premier League and expected to be relegated.
Since making his full debut at Liverpool in December, Mane has started Wolves’ past 11 league games.
They are 17 points adrift of safety with 10 games left, having won only once, and host Aston Villa on Friday.
Wolves need two points to avoid breaking Derby’s Premier League record low points total of 11 in 2007-08.