The 26-year-old, who joined the Foxes from French club Le Havre in 2014, announced in May that he wanted to leave the club.
"The bid was politely declined because it was a low offer," said Shakespeare. "I don't know what it was and I don't get involved."
Mahrez, PFA player of the year in 2016, has reportedly been valued at £50m.
Shakespeare, who is with the Foxes in Hong Kong for a pre-season tournament, had said earlier this week there had been no bids for Mahrez.
The Algeria player made 48 appearances for Leicester last season.
He scored 10 goals and provided seven assists as Leicester recovered from a poor start to finish 12th in the Premier League and reach the Champions League quarter-finals.