The Hampden club have watched with great interest as Hull manager Steve Bruce submitted a series of increased offers for their former player.
They stand to gain £300,000 from the deal, an ironic twist given Stephen Thompson's dismissive approach to the League 2 club's claim for £15,000 when Robertson left the Amateurs for Tannadice last summer.
Thompson angered Queen's in 2010 when he used a loophole related to their status as amateur club to avoid paying a development fee for Barry Douglas. The United chairman made the situation worse by ignoring letters and phone calls from Scotland's oldest club.
Despite clubs such as Partick Thistle, Falkirk and Aberdeen handing over compensation fees in recent years Thompson used the same non-payment approach when he recruited Robertson and Aidan Connolly 12 months ago.
After a period of adverse publicity United offered a closed-door friendly between the clubs at Tannadice as payment with Queen's Park eventually protesting to the SFA and asking them not to register Robertson's and Connolly's move .
A compromise was reached when a fee for Douglas was paid and a 10% cut of any future transfer fee for Robertson agreed.
A spokesman for Queen's Park said: "We can confirm there is an amount due to Queen's Park for any transfer fee received by Dundee United for Andrew Robertson and that amount is percentage related.
"We have not been made aware of any transfer being confirmed so it would be inappropriate to say what our payment would be."
Robertson has remained close to the club that gave him a chance after he was released by Celtic and attended their game against Berwick Rangers in the Petrofac Training Cup last Friday.
The spokesman added: "Andrew and his family have continued to support the youth activities at our club and have regularly attended first-team games as well. We would be delighted for him if he wants to play in the English Premier League and gets a move there."