The midfielder, who has struggled to make an impact this season, could be on the move at the end of the season, with United reportedly monitoring the situation.
Although Chamberlain might not be considered a valuable first-team member of Arsene Wenger's squad, the Gunners should be wary of selling him due to the previous player sales.
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Here are five players whose careers improved after leaving the Gunners and five reasons why manager Arsene Wenger should avoid making the same mistake again.
Thierry Henry was an Arsenal legend, but the finest moment of his club career came after leaving the Gunners in the summer of 2007.
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The Frenchman had snubbed Barcelona the year previously but was granted his wish to join the likes of Lionel Messi, Ronaldinho and Samuel Eto’o over in Catalonia.
His first season was a disappointment, with Real Madrid waltzing to the league title, but the appointment of Pep Guardiola in 2008 ensured they won the treble a year later.
He formed a great partnership with Messi and Eto’o – and later Zlatan Ibrahimovic – and left the Nou Camp with seven new winners medals to his name.
Like Henry, Cesc Fabregas devoted himself to one more year in North London before returning to first club Barcelona.
And, though he struggled to oust Andres Iniesta, Xavi and Sergio Busquets from their starting line-up, he still won silverware away from the Emirates Stadium.
The 28-year-old won the La Liga crown and Copa Del Rey during his two years back in Catalonia and returned to England in the summer of 2014 by joining Jose Mourinho’s Chelsea.
Fabregas then won the Premier League title for Mourinho’s men and, despite failing to reach his usual high standards this year, remains one of the Blues’ most influential players.
It was somewhat of a surprise when Samir Nasri opted to join Fabregas by leaving the club in 2011.
The Frenchman, who had helped the Gunners reach the Capital One Cup final that year, was tickling the fancy of Manchester United but eventually joined rivals Manchester City instead.
He won the league title for Roberto Mancini’s men and won the title for the second time under Manuel Pellegrini in 2013.
Nasri has returned to form and fitness in recent weeks and will be aiming to help City beat Real Madrid to a place in the Champions League final.
Robin van Persie
Never has a player angered the Arsenal supporters like Robin van Persie.
The Dutchman, who was in the form of his life when he signed for Sir Alex Ferguson’s Manchester United in 2012, left the club despite Wenger sticking by him during plenty of injury-plagued campaigns.
Van Persie scored 31 goals across all competitions as Ferguson bowed out with the league title – the trophy he had left the Gunners in order to finally win.
He has since left Old Trafford after struggling under Louis van Gaal but will point to his league title as justification behind his controversial exit from the Emirates.
Like Henry, Ashley Cole was part of the Invincibles side that last won the league in 2004, but he left for Chelsea after having his head turned by Mourinho.
The Blues had eased to back-to-back league crowns when he moved, with defender William Gallas heading to Arsenal in return.
Cole won the league title and FA Cup under Carlo Ancelotti in 2010, but his finest hour came when Chelsea won the Champions League by beating Bayern Munich at the Allianz Arena two years later.
The former England left-back is currently plying his trade in the MLS with LA Galaxy and all in all, has won nine trophies since leaving the Gunners.
Would Alex Oxlade-Chamberlain be more successful away from Arsenal? Have YOUR say in the comment section below!
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