The England international has been in negotiations with the club since last year.
Saka, 21, has played a key role in the Gunners' title challenge this season in the Premier League, scoring 13 goals and providing 11 assists. Arsenal remain in the title race, one point behind leaders Manchester City with three games remaining.
Talks between Saka and Arsenal began last summer, with Saka saying in August that he "shared the same belief" as his manager Mikel Arteta and would extend his stay at the Emirates Stadium.
According to the Press Association, an agreement has been reached between the two parties on a new contract for Saka. The player's current contract expires in 2024.
While Saka is close to extending his contract with Arsenal, midfielder Granit Xhaka could leave this summer. Arsenal could part with the Swiss captain if an acceptable offer is made. Xhaka is under contract with the Gunners until 2024.
