Both Premier League clubs have been linked with the Valencia defender this summer, but according to the latest reports, Chelsea have stolen a march on their rivals with a concrete bid.
The Blues submitted a 25 million pounds offer for the German international according to Spanish newspaper AS. The report adds that Valencia have rejected the offer and are holding out for a fee of 40 million Euros.
Mustafi has a 50 million Euros release clause in his contract.
It has been widely reported that Arsenal are keen on signing the Valencia star, but there has been no official bid from the North London giants so far.
It is understood that Italian outfit AC Milan are interested in the player as well.
Mustafi has been very impressive for Valencia and Germany over the last 12 months and would be a quality addition for all three sides.
Arsenal are without Per Mertesacker for the next few months due to injury and Wenger wants the former Everton defender to replace him.
Meanwhile, Chelsea want him to partner Kurt Zouma at the heart of their defence. The likes of Cahill, Ivanovic and Terry have all regressed and Conte wants to address that position immediately.
Mustafi is training with his teammates in UK now. Valencia will play the likes of Crystal Palace as a part of their pre-season preparations later this week.