Oxalde-Chamberlain, 24, has apparently rejected two offers of £120,000 and £150,000-a-week to remain at Arsenal.
It has also been reported that he has snubbed a £180,000-a-week offer too.
The Daily Star claim after talks with Gunners boss Arsene Wenger, he and his representatives are holding out for more.
Chelsea and Liverpool are said to be keen to capitalise on his situation, with both willing to pay £35million for his services.
Arsenal boss Wenger does not want to lose one of his prized assets to a Premier League rival.

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But The Daily Star say this could potentially be avoided if the Gunners meet his wage demands.
The England international will apparently only accept a £200,000-a-week deal to remain in north London.
It is said he also wants a four-year contract to be put on the table.
Further reports claim Arsenal will decide whether he can move on in the next 24 hours.
But Arsene Wenger backed him to extend his seven-year stay at the club this week.
When asked about Oxlade-Chamberlain’s future, Wenger said: “All these conversations that I have [I say] that I want him to stay and be one of the big players of the future of this club.
“He is one of the players this team has to be built around in the future.
“Personally I want him to commit to the club and to be one of the carrier of the values of our team.
“I want to keep my best players. I only have one target: to keep everybody on board.
“I think we invested a lot of time, confidence and money on players like Alex Oxlade-Chamberlain, who we bought at a young age.
“For me, they have a responsibility for the future of this club because Alex Oxlade-Chamberlain will be one of the big English players in the coming years.
“I personally am highly determined to keep him here at the club and I hope he will commit.”