The Bermuda international has enjoyed a stunning season with 15 goals in 18 appearances since the Bantams won promotion to League One.
A host of Championship clubs have been tracking Wells and January is likely to see Bradford facing a challenge to hold on to their £2m-rated prize asset.
So far, though, only Peterborough have made a concrete bid, the £1m plus offered by Posh chairman Darragh MacAnthony being rejected by the City board without even telling Wells. He later found out when MacAnthony revealed the bid on Twitter.
Parkinson said: “No disrespect to Peterborough – and they certainly had the money from selling Dwight Gayle to Crystal Palace – but Nahki is very ambitious and wants to play at the highest level.
“He didn’t want to move to another club at the same level. He would not have been interested. Facing Peterborough won’t faze him.
“The challenge for Nahki is to keep improving, particularly in terms of his all-round game.
“The higher he goes, the more he will have to improve. That is a fact of life in football.
“Fair play to him, every challenge put in front of him over the past couple of years has been cleared. But we want to go higher and I know he does as well.
“He is someone who loves his football and I know he can keep improving. That is the challenge he faces every day in training.”
Wells’s scoring ability will be tested today against a side who, after a wobble, have returned to winning ways in recent weeks.
Parkinson added: “Peterborough were very unlucky to be relegated last year. They have kept most of that squad, too, so they are a good team at this level.
“I have personally seen them twice recently. The first time, against Walsall, they were awful (in losing 2-0). But then the second time against Tranmere they were excellent (in a 5-0 win).
“So, I have seen both sides of Peterborough but we will prepare for the best one. They have had a few decent results lately and we are expecting a tough game. But one we are looking forward to hugely.”