Gnonto has started just one league game since returning from ankle injury last month and it was against Stoke City, which was the only defeat Leeds have suffered in their last seven league games.
The Italian tried to leave the club in the summer, but the club blocked his sale and he was eventually reintegrated back into the squad by Daniel Farke.
However, speculation is rising that Lazio are interested in signing the Italian winger from Leeds in the winter transfer window.
White conceded that if Gnonto is not getting game time at Leeds then it makes sense for him to seek a move to a club such as Lazio who are a big club in Italy and play in the top flight.
The former Leeds star believes that from a business point of view, it would make sense to sell the winger in January if he is not playing regularly and the Whites get the right price for him.
White said on BBC Radio Leeds: “For sure for him, you are questioning playing in Serie A and playing in the Championship, which one would I want to play in?
“He wants to play for his country for sure.
“If he is not getting regular game time here, he is not getting the best of anything.
“Come January, if he is not playing then I think the question will be how much do we get potentially.
“If the price is right, yes but if it’s not, I think we will hold on to him.
“He was tremendous last season and on a personal note, I’d like to see him wear a Leeds shirt.
“However, from a business point of view and squad point of view, if we can get the right money to seek a replacement then football is a business.”
Gnonto has scored just once in ten appearances in the Championship in the ongoing season, with Farke relying on other options to start.
