Sky Sports, The Guardian, The Daily Telegraph and The Daily Mirror are all reporting that Wenger and Kroenke have come to an agreement after a tumultuous season, which saw a vocal section of Arsenal's support call for Wenger to leave the club.
However, with the season ending on a high with the FA Cup victory over Chelsea on Sunday morning (AEST), it appears the club is now ready to announce Wenger's new deal.
This season was the first time in Wenger's reign that Arsenal missed out on Champions League football, after finishing fifth in the Premier League.
The 67-year-old has been with Arsenal since 1996, winning three Premier League titles, seven FA Cups and reaching the Champions League final in 2006.
Some fans have become increasingly frustrated with Wenger's failure to win a Premier League title since the 'invincibles' side of 2003-04.
Wenger's attention will now turn to re-signing star players Alexis Sanchez and Mesut Ozil who both have one year left on their contract, with Sanchez heavily linked to Bayern Munich.