The Paris-born Algeria forward is likely to command a fee of around £50 million ($65 million, 55.8 million euros), with Roma’s offer believed to be some way short of that figure.
“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, who indicated that he wanted to leave the club at the end of last season, was a key figure for the Foxes on their remarkable run to the Premier League title in the 2015/16 season, scoring 17 goals and making 10 assists, which earned him the PFA Player of the Year award for 2016.
Despite not being as prolific last season, the 26-year-old still chipped in with 10 goals in 48 appearances as Leicester secured a 12th-placed finish and a Champions League quarter-final spot.
Mahrez joined the East Midlands outfit from French side Le Havre in 2014.
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