Until now, Coalition ministers and Whitehall sources have made clear Scotland would lose out on future Ministry of Defence orders if Scots voted to break away from the UK.
The Nationalists argue the quality of workmanship on the Clyde would mean such orders would be secured in an independent Scotland.
Philip Dunne, the Minister for Defence Equipment, told the Commons Scottish Affairs Committee: "We have never placed an order for a warship, other than in times of world wars, outside the United Kingdom. It is not our intent to do so with the Type 26."
Asked by Labour's Ian Davidson, the committee chairman, if Scots voted for independence where would that leave the Type 26 order, Mr Dunne replied: "You raise an interesting hypothetical."
He added: "The future would be more uncertain for all those businesses in Scotland which rely upon UK MoD spend, because we cannot be assured that the security considerations wouldn't lead to some of those decisions to place work in Scotland... would be less certain."
However, Vice-Admiral Andrew Mathews, Chief of Materiel Fleet, asked if the frigates could be built on the Clyde if Scotland was outside the UK, replied: "That's absolutely the case, it depends on the outcome of the referendum and the timing of the 26 order... That is one of the options open to us."
Angus Robertson, the SNP's defence spokesman, said the comments "rightly undermined some of the wilder scaremongering that anti-independence politicians have engaged in".