Potters chief executive Tony Scholes is keen to keep both defenders despite doubts over their futures.
Shawcross is entering the final year of his contract and is yet to agree a new deal.
And Stoke are targeting a permanent deal for Dutchman Martins Indi after he impressed last season on loan from Porto.
Scholes said: “There’s nothing really to say on Ryan apart from he’s been a great player for the club, has been a huge part of what the club has achieved and we hope that will remain the case for many years to come.
“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.
“It’s not just us, there’s Bruno and agent, and there’s the other club as well. Things have to fall into place and everything has to fall into place before a deal is done.
“But absolutely hopeful. Bruno has been a good player for us, but we will have to see.”
Playmaker Bojan’s future is also in the balance after the Spaniard spent the second half of last season on loan with Mainz in Germany.
He said: “I have a contract with Stoke and that gives me security, but what I do is talk to them to find a solution because I have signed until 2020,” said the Spaniard.
“If I have to leave again, the first option is La Liga, where there are very good and competitive teams. We are waiting to see what happens.”
