The defender is unsettled at the Gunners after losing his first-choice status this season.
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It's been suggested White would be open to a move away during the January transfer window.
And Everton are watching the situation.
However, Football.London says management will not consider losing White at this stage in the season.
With Arsenal alive in the Premier League, Carabao Cup, FA Cup and Champions League, manager Mikel Arteta doesn't want to be caught short of options in the second-half of the season.
White's deal with Arsenal runs to 2028, with an option for another year.