HITC Sport understands that a permanent deal could be struck for a man currently impressing during a loan spell at Walsall.
The versatile midfielder, who can play nearly anywhere on the pitch, has been in fine form for League One promotion chasers Walsall - who he joined last month on an initial one-month deal.
Evans's displays were of such quality that Walsall moved to extend his stay until January, but the 20-year-old's form has now captured the eye of a number of Championship clubs.
But Smith - who signed him for Walsall - is leading the chase, with his new club Brentford very much in the mix to land him and with Evans moving into the last six-months of his contract, the 20-year-old could be set to move on a permanent deal with no fresh terms agreed with City.
As well as Brentford, the likes of Sheffield Wednesday, Burnley, Wolverhampton Wanderers and MK Dons are also keen.