Fujitsu is petitioning the Lords for the right to appeal against the decision to send the £11m case for a retrial at the High Court.
The dispute between the two companies hit the headlines after a senior judge at the Technology and Construction Court accused senior Co-op IT staff of taking part in a conspiracy to undermine Fujitsu, then ICL, and lying in court to support their case.
The Co-op won the right to have its case heard again after the Court of Appeal found that judge Richard Seymour believed that nearly all the Co-op witnesses had lied or had acted in bad faith - an approach which meant his "objective vision was distorted".
If the case goes to the Lords, Fujitsu is expected to claim that the criticisms of Seymour made by the Appeal Court do not affect the overall outcome of his judgement and that the Co-operative Group does not have a valid claim against Fujitsu.
The IT services company is also expected to argue that a retrial, possibly followed by another appeal, would extend the dispute for at least another year, and cost both sides hundreds of thousands of pounds in legal fees.
The Co-operative Group said this week that its position had not changed and that it would continue to press for a retrial. It is likely to be several months before the Lords decides whether to accept the appeal from Fujitsu. If Fujitsu is successful, the case is unlikely to reach the Lords before the end of the year.