After an impressive year on loan at Torquay in the National League last season, the 20-year-old has now quickly established himself in the Vale first team under new boss Bruno Ribeiro.
"He's being scouted by Championship clubs," Smurthwaite told BBC Stoke.
"You could see he's come back a man from being at Torquay for a year."
Smurthwaite says that Vale youth product Smith will be offered a new deal by the League One club in the next few weeks, in preparation for what he expects to be firmed-up interest when the transfer window reopens on 1 January.
"I anticipate there'll be some interest in the window, not just at the end of the season," added Smurthwaite. "But it's a long time between now and January.
"There will be a new contract offered to him, as he's on a boy's wage compared to the rest of the squad.
"He's obviously making himself known. And we've been having dialogue with his agent ever since he came in and played his first game in the first team."
Vale stand ninth in League One, on the back of their run of three clean sheets with which they started the new campaign.
Smith has also weighed in with three goals - two in the league and the other in the 1-0 EFL Trophy win over Derby County Under-23s.

Three games were held at Newcastle United's St James' Park and a dedicated Fanzone was created at Science Central.
NewcastleGateshead Initiative said hosting the event had brought a windfall to the city and hotel occupancy reached 99% on match days.
Chief executive Sarah Stewart said the "memorable event" had been a "huge success" for the region.
Ms Stewart said: "I think it's fair to say Rugby World Cup 2015 in Newcastle has been a huge success. From the games themselves to the atmosphere inside the Fanzone, we've had a remarkable two weekends.
"We've welcomed thousands of international visitors who have all contributed to the estimated £43m of economic impact hosting the tournament has brought to Newcastle.
"I have no doubt we'll be feeling the positive effects Rugby World Cup 2015 for many years to come."
The third and final game at the stadium was held on Saturday with Scotland beating Samoa 36-33.
Northumbria Police said there had been "exceptional behaviour" from all those who attended, with very few low-level arrests throughout the event.
Ch Supt Steve Neill said: "I can't thank the fans, visitors and local people enough for their excellent behaviour and patience.
"I am exceptionally proud to have been a part of it myself.
"This is not something that happens on our doorstep every day but everyone in the region has welcomed this opportunity and reaffirmed that the North East is one of the friendliest, most vibrant and safest places to be."
Port Vale chairman Norman Smurthwaite is anticipating "interest" in young defender Nathan Smith following his outstanding start to the season.
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The Rugby World Cup has generated about £43m for Newcastle's economy, tourism bosses say.