The Gunners have been contending with relentless debate surrounding their two prized assets after failing to tie down Ozil or Sanchez to new long-term contracts.
Indeed, the Arsenal pair have six months remaining on their current deals and can start to plot a summer move before the conclusion of the 2017-18 season.
Alternatively, the FA Cup holders could allow the Chile and Germany internationals to leave the Emirates Stadium in January to ensure some return on the Arsenal duo.
Sanchez has been heavily linked with a move to Premier League leaders Manchester City over the past 12 months or so but missed out on a transfer in the summer.
Ozil, on the other hand, has been touted as a potential target for Manchester United given his former Real Madrid boss Jose Mourinho is in charge at Old Trafford.
Former Arsenal defender Keown is tipping Ozil and Sanchez to remain at the north London side beyond the January transfer window.
“The saga of Ozil and Sanchez – please God can it go away so we don’t have to talk about it anymore. I think they’ll stay until the end of their contracts,” Keown told BT Sport.
“They’re that close to it now that I see no benefit in selling them. If they stay then there’s a good chance of qualifying for the Champions League, which is not going to be easy.
“If they go, I can’t see that happening. So I would keep them there to try and position Arsenal in the Champions League for next season.”
Arsenal finished in fifth place in the Premier League table last term to miss out on a place in the Champions League.
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