Price was in the team that lost 4-1 to Birmingham City in the 2010 final, with former Wolves and Northern Ireland striker Amy McCann hitting two of the Blues goals.
A first round bye in the current campaign means that Sunday’s second round trip to Leamington could see Wolves reach the last 16 of the competition.
Against West Midlands League Division One South opposition, Wolves – two tiers higher in the women’s league pyramid – will be expected to go through.
But central defender Price insists that her team will take nothing for granted as they look to chalk up what would be an 11th successive win in all competitions.
“We want to keep our great run going,” says the skipper, “and we’ll go into the game with the same mindset as we do in the FA Cup or League Cup.
“We’ve got a more realistic chance of going all the way in the County Cup than in the bigger competitions, and winning a trophy is one of our aims this season.
“So, we’re taking the game at Leamington very seriously. They’ll be up for it, no question, and they’ll make it as tough for us as they possibly can.
“But we’re prepared for that and we’ll aim to take the game to them. We’ll keep our foot on the gas and hopefully keep our run going in three Cup competitions.”
After Sunday’s game against lower league opponents Wolves will face teams from higher leagues in both the League Cup and FA Cup over the next fortnight.
National League Northern Division sides Stoke City (League Cup) and Fylde (FA Cup) are the obstacles Wolves have to overcome if they are to progress.
“Those ties will be very tough,” says Price, “but after beating Fylde in the League Cup already this season we’ve proved we can compete with teams at that level.
“We can’t be thinking of those games yet, though – it’s Leamington first and we want to get ourselves one game closer to a County Cup final.”