The Frenchman met owner Stan Kroenke on Monday with the club's board informed on Tuesday that he was keen to extend his 21-year reign as manager of the London club.
An official announcement is expected to come from the club on Wednesday, according to the BBC.
The 67-year-old Frenchman, who is out of contract next month, has come in for criticism and calls to go from some fans during a mixed season which saw the club fail to reach the Champions League for the first time in 19 years and finish 18 points behind Premier League champions Chelsea.
But they also won the FA Cup for a record 13th time with a 2-1 win over Chelsea at Wembley.
According to reports, Wenger will start the next chapter of his role by offering Alexis Sanchez and Mesut Ozil bumper packages to tempt the duo to pledge their future to the club beyond 2018.
Sanchez - who scored Arsenal's first goal in the Cup final - will be offered £275,000-a-week to remain at the club with Ozil set to pick up a £280,000-a-week if he agrees to stay on.