The unsettled midfielder asked for a move earlier this summer after an alleged breach of a contract promise at the Britannia Stadium.
His future remains unclear and, following the arrival of Mark Hughes as manager, he may yet opt to stay with the Potters.
Bowen admits he doesn’t know if the midfielder will stay but has offered hope he has a future at the club by saying he has been pleased with his attitude so far in pre-season training.
“Yes, he seems fine,” Bowen told The Sentinel. “People have told me Steven is a quiet lad who does his own thing.
“But that’s contrary to what we have seen, because he’s walking round with a smile on his face and chatting away with the other lads.”
There are several Premier League clubs thought to be watching Nzonzi’s situation closely but, as yet, Stoke have yet to receive any serious offers for the 23-year-old.
Eintracht Frankfurt boss Niko Kovac felt his side could have scored more goals following their 3-0 defeat of Mainz on Saturday.
West Brom manager Alan Pardew refused to fault his players' efforts after a heartbreaking 2-1 loss to Bournemouth that dashed their already slim survival odds.
Cardiff manager Neil Warnock labelled the postponing of his side's clash at Derby as 'scandalous' and a 'disgrace'.