According to journalist Fabrice Hawkins, Martinez has opened "discussions" with Cristiano Ronaldo's Al Nassr and could move to the Saudi Arabian giants after the World Cup.
The Spaniard has been Portugal's manager since January 2023 and won the 2024/25 Nations League following a penalty shootout victory over Spain.
That is the only piece of silverware he's won in charge, although he will want to end his time as manager by lifting the World Cup.
Portugal are one of the favourites for the tournament, but they got off to a poor start on Wednesday evening after labouring to a 1-1 draw against DR Congo.
Newcastle United's Yoane Wissa cancelled out Joao Neves' sixth-minute header on the stroke of half-time, and then the Portuguese couldn't find a winner.
Martinez's persistence in playing Ronaldo, despite him being non-existent in matches, arguably cost them against Congo and could cost them a shot at winning the World Cup.