Maloney’s club Chicago Fire rejected the English Championship outfit’s opening offer last week but Hull manager Steve Bruce is refusing to throw in the towel over his attempt to land the 32-year-old.
Bruce is hopeful he can persuade Maloney to return back across the Atlantic just seven months after the former Celtic player joined Fire in a £1 million switch from Wigan.
Speaking recently, Bruce said: “He is another one that we hope that we can get that over the line. He’s somebody I have liked for a long time.
“We know we’re thin on the ground but I’m still confident that by the end of the window we’ll have enough in the building to make sure we can mount a challenge.”
Maloney made his 14th appearance of the MLS season in Chicago’s 1-0 defeat by Philadelphia on Wednesday.
Meanwhile, Ross McCormack is set to be rewarded with a new and improved deal at Fulham.
Eyebrows were raised when the recently-relegated Cottagers paid in the region of £11m to sign the Scotland forward from Leeds last summer.
However, McCormack has impressed in west London, leading to reported interest from Norwich City and Middlesbrough.
The Championship outfit have acted to secure the 28-year-old’s future, though, and a new contract is thought to be imminent.
McCormack signed a four-year deal upon arriving at Craven Cottage last summer, with the option of a further 12 months.