The Scotland international was linked with a move to Hull City, who reportedly lodged a £12m bid to sign the striker, but Rovers rebuffed their advances to keep him at Ewood Park.
"Jordan's the kind of lad who doesn't let anything bother him, he just gets on with it," Marshall told the Lancashire Telegraph.
"He's just a down-to-earth lad. He didn't go anywhere so he's just got on with it and done his job. Of course it was a massive boost to keep him, we all didn't want him to go.
"He's here now so hopefully he can push on keep getting the goals."
Rhodes has scored four goals in eight matches for Rovers this season.