Spanish outlet Marca, along with Sky Germany and Bild, report that the Bundesliga club have reached an agreement with Martinez, who is set to arrive from Toulouse to take charge at the BayArena.
Martinez is currently out of contract after completing a three-year spell in charge of the French side. He is expected to sign a two-year deal with Leverkusen as the club look to begin a new era.
The 42-year-old has built his reputation through coaching work in youth development, having previously been part of the set-ups at Espanyol and FC Barcelona before stepping into senior management.
At Leverkusen, he is expected to succeed Kasper Hjulmand, who has not yet been officially dismissed but is widely reported to have no future in the role. The Dane's position has been uncertain for some time, with the club already preparing for a change in leadership.
French Ligue 1 side Auxerre have confirmed that Moroccan midfielder Oussama El Azzouzi will return to parent club Bologna following the conclusion of his season-long loan spell.
RB Leipzig sporting director Marcel Schafer has moved to calm speculation surrounding head coach Ole Werner, insisting there is no rush to make a decision on the manager's long-term future.
Alejandro Grimaldo has reaffirmed his ambition to end his career in LaLiga, with the Bayer Leverkusen defender maintaining that a return to Spain's top flight remains a key long-term objective.
Alphonso Davies has moved to ease concerns over his fitness after linking up with the Canada squad ahead of the 2026 World Cup, saying he is focused on recovery rather than rushing back into full action.
