The Scotland international moved to Ewood Park last summer in an £8million deal from Huddersfield Town.
He hit 28 goals in all competitions for the Lancashire club despite their relative struggles last season, prompting speculation a big money move to the Premier League may be in the offing this summer.
West Brom, Fulham, West Ham and newly promoted Hull City have all been linked with a move for the 23-year-old in recent weeks.
New Rovers boss Gary Bowyer has already spoken of his desire to keep Rhodes at Ewood Park, while the player himself has shown no indication that he wants to move.
When asked about Rhodes' situation, Rovers chief Shaw insisted that he had received no bids for the frontman.
"As things stand we have had no official approaches from any club for Jordan," he told the Lancashire Telegraph.