Since first moving to the Potters on loan in 2007, Shawcross has made 380 appearances for the club in all competitions but the club captain has just 12 months remaining on his current deal.
Scholes has said that efforts are being made to tie up the player's future, but he has warned that it could be a "long process".
"When you've got important players, you want to do something sooner rather than later, but that is a very simple statement about what can be a very complicated and long process," he told the Stoke Sentinel.
"There's always talks. People talk about 'have talks started?' We've been in contact.
"He's been a great player for the club, he's been here a number of years now, been a huge part of what the club has achieved over the years and we hope that will remain the case for many years to come."
During the most recent campaign, Shawcross made 38 starts in all competitions.