United have agreed a £73m transfer with Borussia Dortmund for the 21-year-old winger, who will join after England's Euro 2020 final defeat to Italy on Sunday.
"People might suggest he'll feel added pressure at United because of his price tag, but I don't agree," Ince told the Daily Star.
"He doesn't decide how much he costs, so it won't affect him mentally.
"Look at how much United spent on Donny van de Beek and Fred.
"Getting Sancho for £73million could be a bargain. If he performs the way he's capable of performing, they can always sell him on for double!"