Mikel Arteta is thought to be keen to add another centre-back, despite signing Pablo Mari from Flamengo in January.
Liverpool have reportedly held strong interest in White for some time and are weighing up a bid of their own.
The amount of interest White has is indicative of his standout performances in the Championship so far this season.
White has started all 37 league games for Leeds so far this season and has played every single minute of the campaign.
The Englishmen has even been used as a defensive midfielder at times this season, such is how Bielsa sees his technical ability.
He also came up against Arsenal in the FA Cup tie at the Emirates Stadium not too long ago.
Arsenal's defensive record has begun to improve under Arteta and players that were struggling have looked more confident.
David Luiz has looked more like the leader he was at Chelsea, whilst Shkodran Mustafi is enjoying a good run of form.
However, Arsenal are understood to want more emerging defensive talent to complement William Saliba, who will arrive from St Etienne this summer.
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