The Scottish champions are believed to have made the former Dutch national coach a substantial offer although as yet they have failed to make an official approach to PSV.
The Dutch champions' chairman, Harry van Raay, appears resigned to losing the 50-year-old Advocaat, who will make a decision after next weekend's home game with Ajax. He has urged his Rangers counterpart, David Murray, to pursue his interest through more official channels.
"I'm now waiting for a phone call from Scotland," he said. "If it doesn't come, then I expect Dick Advocaat to remain at PSV next season.
"I am not yet drawing any conclusions, but it will be a tense time while I await that call from Glasgow. We will naturally take any offer from Rangers into serious consideration."
Van Raay also made it clear that he was unhappy with the manner in which negotiations had been conducted. He added: "If they call, I will make it clear that they should have called me before they opened negotiations with him. That's the rules."
Despite his anger at the situation, Van Raay confirmed that Advocaat has a clause in his contract allowing him to leave should he receive a better offer for his services. It now appears only a question of when Advocaat would be free to leave Eindhoven, with the likelihood of him staying on until the end of the season before making the switch to Glasgow.
Rangers lead the Bell's Scottish League Premier Division on goal difference from Celtic and Hearts, although their quest for a 10th successive title looks fragile after Saturday's 1-1 home draw with Dunfermline. Their chairman, David Murray, was unavailable for comment yesterday, although he has previously insisted he will make an announcement regarding the managerial position "when the time is right."
Jocky Scott, the former Arerdeen and Hibernian manager, will today will become the manager of Dundee for a second time. He is ready to move from his coaching position at neighbours Dundee United to take over from John McCormack, who was sacked on Sunday.
Dundee are five points clear at the top of the First Division. McCormack said: "I do not know why I have been sacked. I was given no reason and I have done nothing wrong.
"I was told only that the board wanted to go down a different road. Then they told me to clear out my desk and asked me to seek legal advice."