Rangers have refused to accept briefs at the request of their fans for the February 2 clash at Tannadice in protest at what they believe was unfair treatment from the United board in the summer as the Ibrox club imploded.
However, United have decided to ignore official club channels to sell briefs direct to Rangers fans and have set aside an away section in the ground, sparking Green's fears of tensions on the terraces.
The Ibrox chief executive lashed out at United chairman Stephen Thompson and his board saying: "Football needs to be safe and there's no guarantee it will be. It wouldn't need a bright guy to tell you that there has been tension between Rangers and Dundee United for a number of years. We have taken a decision to defuse that tension.
"But the decision to sell tickets to people who may not be Rangers fans is taking it to a high level. We have been very clear from day one. Because of the fans' issues with Dundee United and as a board we made the decision not to take tickets and requested they didn't make tickets available to Rangers fans.
"We are concerned that Dundee United won't know who they are selling tickets to and how will they know if they're genuine Rangers fans or potential troublemakers?
"The reason is because if we're not selling the tickets then we're not convinced that someone on the outside has that control. It's safety-driven."
United chairman Thompson, who called in police last summer after receiving death threats, declined to comment, but his club released a statement. "While we remain disappointed with the position of Rangers in respect of not taking any tickets for this match, we will not make any statements which may inflame the situation, particularly to avoid encouraging any hostility between our two sets of supporters.
"Now that ticket prices have been agreed, we hope that everyone can now focus on a game of football. Although Rangers do not wish to take a ticket allocation for this match, opposition fans are always welcome at Tannadice and we will be happy to reserve an appropriate section of the stadium for any Rangers fans who wish to attend this fixture."