The chief executive of O2, Ronan Dunne said it's unlikely that Hutchison Whampoa, parent company of Three, will buy the network.
O2 and EE have been the subject of acquisition talk with Hutchison and BT are emerging as the front runners.
However, Dunne put stops to rumours it would be bought by Hutchison, saying at a media dinner: "Of all the scenarios in the market I think it's the least likely.
"At the back end of last year some analysts told me that their main prediction for this year was that Three will buy O2. All I would say is I slept very soundly that night."
Dunne went on to say that only having three or four mobile networks operating in the UK is unlikely and it's preferred by mobile networks to have four so competition isn't as tight.
In other countries, such as Germany and Ireland, there are fewer mobile networks and special conditions apply to ensure no single network is dominating unfairly.
O2's parent company, Telefonica has been on the lookout to sell a number of its assets, including its UK operation, in a bid to cut its debt and improve its credit rating.
Last week, BT confirmed it was in talks with O2 to take the network over, saying in a statement: "We have received expressions of interest from shareholders in two UK mobile network operators, of which one is O2, about a possible transaction in which BT would acquire their UK mobile business," the statement added.
The other party is thought to be EE, although as Hutchison Whampoa already uses the leading 4G network for its 3G services, it's more likely the company will become part of Three in the UK.
