Evans, 28, started his career at Manchester United and was playing there up until 2015 when he made the move to the Midlands based club.
Arsenal were successfully swatted away a year ago, while Leicester have seen two bids rejected earlier in this window.
"It doesn't [surprise me] and it's quite refreshing that Man City are trying to buy a British or Irish player because we always see these foreign imports coming in who don't know the Premier League", Given said.
Evans has two years left to run on his current deal at the Baggies.
"But this time previous year, Arsenal were interested in him as well".
Nonetheless, Evans still made 198 appearances for the Old Trafford club, winning three Premier League titles, two League Cups and a FIFA Club World Cup. Evans, however, could be a valuable addition to the first-team setup at Etihad.
While they have managed to reinforce the full-back positions with the arrival of Kyle Walker, Benjamin Mendy and Danilo, the heart of defence is still understaffed, with John Stones, Nicolas Otamendi and Vincent Kompany the only senior options at Pep Guardiola's disposal.
Jonny Evans would be a good signing for City.
The BBC report that early talks have already taken place between City and Evans' representatives but an agreement on a fee has yet to be agreed upon for the West Brom defender.
Evans drew interest from City's Premier League rivals Arsenal last summer, although their approach was also rejected.