Stoke dismissed Hughes following their FA Cup third-round defeat to League Two side Coventry City on Saturday with the club also in the Premier League relegation zone.
"They have to get the manager in very quickly because he's going to want to go out and spend some money in the transfer market, there's no doubt about it," Higginbotham told Sky Sports News.
"He [Peter Coates] is not a chairman who hires and fires quickly. He obviously thinks about what he's going to do and the decision has been made now.
"You would have thought with the timing of Hughes' sacking, they would have somebody in mind because the new manager that comes in is going to want to spend money in this January transfer window and get signings that are going to be key to hopefully keep Stoke in the Premier League."