Crystal Palace are admirers of the 21-year-old, having monitored the midfielder for some time, as he starred for Ipswich in League One.
The Eagles stepped up their pursuit for Downes this summer, making offers to the Tractor Boys for the young midfielder in a bid to take him to Selhurst Park.
Crystal Palace’s latest bid for the Brentwood-born youngster is said to be worth around the £2m mark.
However, Ipswich have rejected both offers from Roy Hodgson’s men.
Frustrated by the club’s rejection of the two offers, Downes has now handed in a transfer request as he looks to force his way out of Portman Road.
Ipswich are claimed to value the 21-year-old at £4m, which is double the amount that Crystal Palace offered in their latest bid.
Downes made 32 appearances across all competitions for Paul Lambert’s side last season, scoring and assisting twice.
