Lawn told the Yorkshire Post: "The possibility of us becoming involved with Odsal was mentioned to me by the council and it would be naive not to investigate it.
"It is my impression that a decision will be made over whether the scheme gets the go-ahead in the next couple of weeks and that the signs are encouraging.
"Our possible involvement would be in the long term obviously and we have not even had any projected figures from the council. But it is something we have to look at - not least because of the huge overheads involved with running Valley Parade."
It has been reported that Bradford Council are hoping the complex, which would incorporate facilities for cricket, athletics and cycling, can be completed in time for the 2012 Olympics and that Sport England are "very supportive" of the scheme.