Bolger, yet to make a first-team appearances for the Foxes, joined the npower League Two club on loan for a third time in September.
Ward would like to keep the 20-year-old Irishman at the Memorial Stadium and told BBC Radio Bristol: "We've bid for Cian to bring him in but Leicester have turned it down."
Asked about the possibility of making another offer for Bolger, Ward added: "I'm not sure if we can go and improve on that bid at the moment as the cash flow is not as nice as we'd like it."
Republic of Ireland Under-19 international Bolger has been restricted to just four appearances this season because of injuries but has recently recovered and featured in Ward's first win as Rovers manager against Plymouth on New Year's Day.
- Sports & Recreation