On Wednesday, the High Court approved the Â£84m takeover by utilities giant Severn Trent.
However, shareholders of the Wrexham-based company, who called it a "David versus Goliath" dispute are appealing.
Any application to appeal must now be made by Monday and the case will be heard by 22 February.
Some staff and customers had opposed the move amid fears for jobs and an increase in bills.
Customers pay an average of Â£145 a year for their water compared with Â£172 for Severn Trent.
Dee Valley Water employs about 180 people and has 230,000 customers across the Wrexham and Chester areas.
Opponents of the takeover of Dee Valley Water have been granted leave to appeal the move.