The ambitious Chinese outfit had already secured the signature of Chelsea striker Nicholas Anelka at the beginning of the month and were ready to offer Upson a lucrative deal to move to Asia.
However, Shenhua were left disappointed in their pursuit of the 32-year-old after no agreement could be reached with the Potters.
Pulis rbought Upson to the Britannia Stadium on a free transfer over the summer after West Ham United opted against extending his previous contract.
And the Stoke manager is hoping any uncertainty regarding his future can be put to one side until the end of the season.
"He knows what's going on, there's no hidden secrets," Pulis said in The Sentinel.
"It was an unbelievable offer and he had to look at it. But the club wanted money for him and that was between Matthew and the club.
"He's got another year left on his contract with us and I've always said how pleased I have been with him, both on and off the field."
Upson has found first-team opportunities hard to come by under Pulis, with the Stoke boss opting to continue with Ryan Shawcross and Robert Huth at the heart of the defence.
