Wells broke a 51-year club record by scoring in eight consecutive matches on Saturday when his double helped Bradford register their first league win over Sheffield United in over 25 years.
The Bermuda international, 23, signed a new three-year contract with Bradford in September last year and has been the subject of transfer speculation throughout the summer after registering 26 goals last season.
"It is a terrific achievement and we shouldn't hide away from the fact that he is a very dangerous striker," Parkin said after Saturday's 2-0 win.
"We are proud to have him and we are going to work to keep him here.
"It is a very proud record for him to hold and he scored two goals that show why he is a good striker.
"The first one was a goal of sheer class and quality and his second goal was a scruffy poacher's effort."