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.
Christian Eriksen is "doing well" after collapsing during Denmark's friendly against Ukraine, with the match abandoned amid distressing scenes in Odense on Sunday evening.
Germany midfielder Lennart Karl has confirmed he will miss the 2026 FIFA World Cup after suffering a thigh injury during training, bringing a painful end to what had been a remarkable breakthrough season.
Julian Brandt's departure from Borussia Dortmund has opened the door to fresh transfer speculation, with the German international reportedly offered to Lazio as he prepares for the next step in his career.
Nathaniel Brown has refused to be drawn into speculation linking him with a move to Bayern Munich, insisting that his full attention remains on Germany's upcoming FIFA World Cup campaign.
