The pair are out of contract at the end of 2019-20 but opened talks over new deals before the coronavirus pandemic.
Bullen believes both want to stay.
“I think both lads are really happy and their families are really happy, so we are very, very confident that something can be done,” said Bullen, who started the season as caretaker manager until the appointment of Garry Monk.
“But ultimately, until something is signed, you just never know. You never know who could come out of the woodwork and offer them something out of this world. Talks are positive and well down the road.”
Fox and Fletcher are the only ones from a long list of players out of contract this summer the Owls have acknowledged opening talks with.
FIFA are expected to try to regulate so that if, as seems likely, Covid-19 drags the 2019-20 season beyond June 30, contracts are extended accordingly.
Club finances across the leagues imperilled by the lack of football during the pandemic and the Owls are one of many sides yet to reach agreement with their players over wages, but Fox and Fletcher have done a good job for them – and, Bullen points out, the same is true in reverse.
Fox looked to be on his way out in the summer but has established himself as the first-choice left-back.
Fletcher is Wednesday’s top-scorer this season as he was last, and his value was never more obvious than when he was missing through injury at the start of 2020.
The Scotland international joined on a free transfer after being released by Sunderland in the summer of 2016, 12 months before Fox joined from Charlton Athletic.
”Both lads have had fantastic seasons,” said Bullen. “That’s in part down to themselves, but it’s also in no small part down to the football club in supporting them.
“Foxy went through a hard time and Fletch last season obviously had one or two injuries and never really got going. This season he’s been fantastic, he’s overcome that injury and is coming back to full fitness.”