Kevin Hollinrake, the Conservative MP for Thirsk and Malton, said he planned to write to Sir Terry Leahy, the former Tesco boss who is leading the bid from Clayton, Dubilier & Rice (CD&R), to ask him to set out clearly his plans for Morrisons.
Mr Hollinrake told The Yorkshire Post: "I am not against private equity investment but we have to make sure they do not benefit from any in-built tax advantage. We must do more to establish and maintain a fair and level playing field for all businesses that operate in the UK."
Yesterday, a spokesman confirmed that Morrisons will continue to pay taxes in the UK if it is taken over by CD&R.
CD&R has reiterated that Morrisons' head office will stay in Bradford if its bid is successful.
A spokesman said: "Should CD&R assume ownership of Morrisons, the company will remain headquartered and registered in the UK and continue to pay taxes in the UK."
Earlier this month, Morrisons confirmed it was in discussions with the stock market’s Takeover Panel to launch an auction process for the chain.
Bosses hope to bring to an end the three-month battle for the business between two private equity firms, Clayton, Dubilier & Rice (CD&R) and Fortress.
Morrisons said that, on the basis that neither bidder has declared their offer final, “such that either offer may be further increased or otherwise revised, a competitive situation continues to exist”.
As a result, the company has started talking with the Takeover Panel and the bidders “in order to begin discussions around an orderly framework for the resolution of this competitive situation”.
Shareholders will vote on the deal in or around the week of October 18, the supermarket added.
Bosses continued to stress that any bidder must uphold the group’s values.
In a statement issued earlier this month, the supermarket said: “In addition to the financial terms of any offer, the Morrisons board continues to place very significant emphasis on the wider responsibilities of ownership of Morrisons.
“These responsibilities include a recognition of the importance to the Morrisons business of all stakeholders, including colleagues, customers, pension trustees and suppliers as well as the distinct heritage and history of Morrisons and the legacy of Sir Ken Morrison.”
The takeover process started in June with CD&R making a £5.5 billion bid for the business.
This was followed by a bid of £6.7 billion by Fortress and a counter bid of £7 billion from CD&R.
Fortress has previously said it “continues to consider its options” but has not made a further announcement.