The Birmingham Mail says Given has been patient but is now keen to kickstart his stalled career and in that respect, with only Brad Guzan and Andy Marshall in reserve, Villa represent a decent option.
Having settled on Given as their first choice Villa must now agree a fee with City for a player who has more than two years left on the contract he signed when he joined the FA Cup winners from Newcastle in 2009.
City paid £7m for him then and will want to recoup much of that since they will have to find a replacement themselves.
Another sticking point could be Celtic's interest. Just last month Given spoke glowingly about the Scottish club although they would not be able to match the financial package Villa could put together.