Gers boss Ally McCoist is interested in landing the 30-year-old, who is out of contract at the end of the season, this summer.
United have confirmed they have received a letter from Rangers informing them of their intention to speak to the player about a pre-contract deal.
The Irn-Bru Third Division leaders are not allowed to sign anyone for money due to a 12-month transfer ban imposed by the SFA for non-payment of taxes.
However, the Glasgow club are allowed to register free agents after the next transfer window closes on August 31.
The former Republic of Ireland Under-21 international, who is the captain at Tannadice, can play either up front or in the heart of defence. McCoist has been concerned at how softly his team has conceded goals during the 2012/13 campaign and has vowed to strengthen his rearguard.
Despite his contribution up front, Daly has often been utilised at centre-half and would give Rangers another option in that crucial department.
McCoist currently only has Chris Hegarty, Ross Perry, Emilson Cribari and Lee McCulloch who can play in that area.
However, the Dubliner, who has scored 57 goals in 158 appearances for United since joining them in 2007, has not agreed to the move yet.
And it remains to be seen if he would be happy taking the step down from the SPL in the 2013/14 campaign.
His representative, Eamonn Collins, will talk to Rangers about the switch to the lower leagues – but his client also has the option of a move abroad.
Meanwhile, financial expert David Glen today claimed Rangers' interim results show Charles Green was correct to examine selling the naming rights for Ibrox.
Rangers yesterday announced they had made a loss of £7million for the last seven months of 2012.
Glen believes that underlines that Green, who has confirmed that Sports Direct will be the stadium sponsor, was right to take the controversial step.
He stated: "Renaming the stadium is quite an emotive issue. But if there are areas where you can make money in this difficult financial climate then I think that you have to exploit them.
"Since it was revealed that Rangers were considering selling the naming rights to Ibrox a lot of folk have asked: 'If there is £21million in the bank whey do you need any more?'
"But, for me, from a financial perspective, they have to examine every opportunity there is and they have done that."
Glen added: "Rangers will grow stronger, but they are not going to see vast profits in the next couple of years. They will have enough to see themselves through.
"I still believe some of that £21million they raised from the share issue last year will need to be used for the running of the club as they bid to get back to the SPL."