Evans was heavily linked with a move away from West Bromwich Albion during the summer, and the Baggies again look like facing a battle to keep their star player this month.
Arsenal have long been interested in the Northern Irishman as they look to bolster their leaky defence, particularly after recent injuries to Nacho Monreal and Laurent Koscielny exposed a lack of depth at the back.
However, the Gunners face stiff competition for his signature from Premier League leaders Manchester City, who are also keen to improve their defensive depth due to the ongoing injury troubles of Vincent Kompany.
The Times reports that Arsenal are now increasing their efforts to bring the 30-year-old to the Emirates Stadium, with West Brom understood to want at least £25m for his services.
However, Evans himself is thought to favour a move back to Manchester as he lives in the North-West following his 11-year spell as a Manchester United player earlier in his career.
Evans joined West Brom from United in 2015 and has gone on to make 84 appearances for the club across all competitions.