The 31-year-old has been a key player for the Gunners for the past five years and his form has been brilliant this campaign.
Partey recently stood out in the Champions League quarter-final ties against Real Madrid. The club now want to reward him for his efforts.
His current deal expires at the end of June and the club could discuss an improved contract for another two seasons at least.
They could propose a two-year contract or a one-year deal with an option. Partey is prepared to negotiate fresh terms with Arsenal.
If a renewal does not materialise, Partey could have plenty of proposals to consider. He is on the radar of several Saudi clubs.
Atletico Madrid have also been credited with an interest in re-signing him. Diego Simeone remains a huge admirer of his services.
Partey could be tempted to reunite with the La Liga giants.