Queen Elizabeth II hopes Scotland will "think very carefully" about their decision on whether to become an independent country in a closely-watched referendum, British media reported on Sunday.

The queen was reported to say to a well-wisher "I hope people will think very carefully about the future," after attending a church service near her Balmoral estate in Scotland.

Polls show the campaigns for and against independence are neck-and-neck, and both sides have thrown efforts into a final drive to win over undecided voters.

The pro-independence Scottish National Party has said that if the country becomes independent it will be up to voters whether to retain the monarchy or not.

After press reports claimed the queen was concerned about the September 18 referendum, Buckingham Palace issued a statement on Tuesday saying she would remain impartial on the subject.

"The sovereign's constitutional impartiality is an established principle of our democracy and one which the Queen has demonstrated throughout her reign," the statement said.

"As such the monarch is above politics and those in political office have a duty to ensure this remains the case.

"Any suggestion that the Queen would wish to influence the outcome of the current referendum campaign is categorically wrong. Her Majesty is simply of the view this is a matter for the people of Scotland."