Parkinson's current deal is due to expire at the end of the season, and he is now a coach in demand - with Championship side Blackpool having already made one approach for his services.
Bradford's exploits in the Capital One Cup have seen the former Charlton manager's profile rocket.
The Bantams booked their place at a Wembley final by seeing off Aston Villa on Tuesday, with the League Two outfit having made their own bit of history.
Lawn is confident that Parkinson will lead the club into that cup final, and is also optimistic regarding the possibility of putting a contract extension in place.
"His contract is up. We have been talking to him already. We are in negotiations," Lawn told Sky Sports after seeing Bradford wrap up a 4-3 aggregate win over Villa.
"Blackpool approached us and said that they wanted to speak to him. We asked Phil if he wanted to speak to them, which is only fair, and he said no he didn't. He said that he wanted to stay with us.
"He can see that this is the start of something and that we are building something. He wants to do that. If we can possibly do that, we'll do that."