According to the Daily Mail, Middlesbrough are holding out for a package of £20 million up front plus a further £5 million in performance-related bonuses for the midfielder, who was named Championship Player of the Season this year.
Hackney, 23, is understood to prefer a move to Everton despite interest from Crystal Palace and Hull City, with the Echo reporting that David Moyes' side remain the player's first choice destination.
The gap between the two clubs' positions is significant but not insurmountable.
Middlesbrough's stance is in part driven by the precedent they set last summer, when they were willing to sell Hackney to Ipswich Town for £20 million.
The England Under-21 international turned that offer down to remain at the Riverside Stadium, where he excelled under new manager Kim Hellberg and led the club all the way to the Championship play-off final.
Boro lost that final 1-0 to Hull City at Wembley, but Hackney's status as the division's standout midfielder was beyond dispute by the end of the campaign.
Crystal Palace are also expected to enter the race formally, with reports suggesting the Eagles have indicated a willingness to bid around £20 million — particularly as they brace for potential interest in their own central midfielder Adam Wharton from Liverpool.
Outside observers have suggested a fair market price for Hackney might sit closer to £10 to £12 million given that he enters the final year of his contract this summer, which would give any potential buyer leverage.
Middlesbrough, however, are clearly willing to test that theory. The club's strong stance reflects both the level of interest in Hackney and the financial reality of needing to replace him if he leaves.
Hackney came through Middlesbrough's academy and, aside from a loan spell with Scunthorpe United, has spent his entire career at the club. His importance to their promotion hopes next season makes the case for selling him considerably more complicated than the raw contract situation might suggest.
Everton's midfield position also adds context to the pursuit. Idrissa Gueye's contract expires at the end of the month, while Tim Iroegbunam has attracted interest from elsewhere, with Ipswich Town among the clubs reportedly monitoring the 22-year-old.
Separately, young winger Isaac Heath has departed Everton on a permanent basis, joining League One newcomers Cambridge United for an undisclosed fee.
The 21-year-old joined the Blues aged 13 and developed through the club's academy before a highly productive loan spell at Accrington Stanley in League Two last season, where he won the club's Young Player of the Season, Players' Young Player of the Season and Manager's Young Player of the Season awards.
Whether Everton can bridge the gap on Hackney will likely come down to how much they are willing to move their guaranteed fee upward — and whether Middlesbrough's nerve holds when the next offer arrives.