Chelsea captain Terry retired from international football on the weekend and Begovic feels that 24-year old Potters skipper Shawcross is the perfect man to slot into central defence.
"There is no-one better to fill that void now," Begovic told the Stoke Sentinel.
"Ryan has been a captain at our club for a long time and that speaks volumes for his leadership qualities.
"Hopefully, he will get a bit more consideration now and he will become a regular in the England squad.
"First and foremost Ryan is a quality defender and I think that is what some people tend to get away from these days.
"England couldn't do too much wrong by picking Ryan.
"He leads by example. He is not the loudest of guys around the dressing room, but he does what he needs to."