Adams's current deal is due to expire at the end of the season and Smurthwaite wants the 52-year-old to make a decision on his future by the start of March at the latest.
"I genuinely believe he wants to stay, I want him to stay," Smurthwaite told Signal Radio. "There is something on the table there, which is there whenever he wants to come and have a look at it.
"He will have to make a decision at the latest at the end of February or early March because operationally, if he doesn't wish to stay or doesn't choose to sign the contract that's in front of him, then basically I will then have a contingency.
"But it is my belief he wants to stay. I believe he will be there next season and hopefully for some time to come."
Adams is currently in his second spell as Vale boss, having left the Burslem club in December 2010 before returning in May 2011 following a brief stint in charge of Sheffield United.