Evans is wanted at the Emirates Stadium this month to help bolster Arsene Wenger’s backline.
Wenger is on the lookout for new recruits at the back with Per Mertesacker retiring at the end of the season.
And Starsport understand an offer of £10m plus right-back Mathieu Debuchy has now been made for the Northern Ireland international.
Manchester City are also keen on Evans but have turned their attention to Aymeric Laporte instead.
The Gunners know West Brom need to sell Evans if boss Alan Pardew is to have any cash to spend.
Jonny Evans next club odds
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“Arsenal have bid £10m and Mathieu Debuchy for Jonny Evans”
They’re also aware of a relegation release clause in the player’s contract which would mean he’d be free to leave for just £3m if the Baggies go down.
Evans also has just 18 months left the contract he signed when moving from Manchester United for £6m in 2015.
Pardew admits a sale could be on.
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Speaking earlier this month, the Hawthorns chief said: “The position at this football club financially is very, very tight.
"We might have to move a player out to bring players in.
“I’m saying we need to bring players in.
ARSENAL FC
“We have to be on our guard for a bid of any player that might interest us."
Arsenal have until 11pm Wednesday to get a deal done.
However the'll want the transfer sorted ahead of the deadline, as West Brom travel to Manchester City that evening for an 8pm kick-off.