The company will consider whether to go ahead with an appeal after the High Court clarifies its ruling at a hearing on Wednesday.
Last week's decision was a blow to Ian Grice, Alfred McAlpine's chief executive, who oversaw the rebranding when he took up his position in August.
Garry Forster, group company secretary of Alfred McAlpine, said that he was pleased that the leave to appeal had been granted, and that the company would consider its options.
Forster said that it was determined in court that Alfred McAlpine would not have to make any changes to its corporate identity immediately.
But he noted that the ruling stipulated that its website must be changed before the beginning of May and the company logo by the end of July.
He said: "We will have to sit down in the next few days and decide what our next course of action is going to be, based on what has been decided today."
Forster said that the legal bill for both sides had reached £1.1m, but that Alfred McAlpine had not calculated the cost of its rebranding. He added that Sir Robert McAlpine had not sought damages.
James Withey of brand consultant Landor suggested the best option for the firm would be to accept defeat and look at a different change to its brand identity. He said: "If it rebrands for a second time, some of the work to research where the company is at the moment is not lost."