According to John Cross in the Mirror, the Gunners are confident they can convince the midfielder to remain at the club and are prepared to offer him new terms worth in excess of £100,000 per week—his contract expires next summer.
Cross added that Arsenal manager Arsene Wenger has made moves to tie down Oxlade-Chamberlain, 23, to a new contract "within the next few weeks."
Paul Joyce in The Times previously reported Oxlade-Chamberlain was tempted by the prospect of working under Liverpool manager Jurgen Klopp and had "concerns about his career development if [Wenger] remains in charge."
Wenger penned a new two-year deal with Arsenal on Wednesday:
B/R Football @brfootball
BREAKING: Arsene Wenger agrees two-year contract extension with Arsenal, the club has confirmed https://t.co/647PYx3Etf2017-5-31 12:31:49
However, the England international has seemingly been convinced that the Emirates Stadium remains the best place for him, and Cross suggested Wenger's picking him to start the FA Cup final victory over Chelsea was an indication of the Frenchman's determination to keep him.
The former Southampton player joined Arsenal in 2011 to great excitement given his talent.
He has failed to fulfil his immense potential but enjoyed arguably his best campaign in 2016-17, performing particularly well in the latter stages as he operated as either a central midfielder or a wing-back.
Still, Oxlade-Chamberlain only started 16 Premier League matches in 2016-17, making 13 appearances as a substitute in the English top flight, an indication that he remains only a squad player rather than an indispensable part of the first team.
However, he clearly feels it is best for him to stay with Arsenal as he reaches the peak years of his career, and given how he finished last season, he could finally become a guaranteed starter next term.