A takeover battle for Alliance Boots by private equity firms is "anxious and unsettling", union leaders say.
Boots is one of the UK's most recognisable High Street brands.
The union Usdaw said workers were worried about how the bids would affect long-term job security and pensions.
A £10.6bn bid by Kohlberg Kravis Roberts (KKR) was backed by the firm's board, but a Nottingham MP said it was too early to draw conclusions.
Private equity consortium The Wellcome Trust and Terra Firma later made a rival proposal worth £10.8bn.
Broxtowe MP Nick Palmer said any new owners needed to expand the business and not asset strip the business.
"If there is a successful bid, the new management should expand the company instead of asset strip it and ensure the pension fund is fully financed," Mr Palmer said.
"We will press the new owners as soon as possible. Other takeovers have resulted in long periods of uncertainty - and that would be unsatisfactory."
KKR said in a statement that it intends to expand the company and make it a global leader.
"In the years to come if we own the business, we will employ more people in the future than we do today."
Usdaw general secretary John Hannett said he had written to senior Boots' directors "seeking an urgent meeting to clarify what a successful bid might mean for Usdaw members".
"Basically what they'll want to know is what is the intention if this bid is successful, for their job security, their pensions and so forth .. and let's see whether this is a growth strategy or is it an asset-stripping strategy.
"Our members are less concerned about who makes profits than making sure they can continue to have a job to support their families," said Mr Hannett.
'Worth a fortune'
Martin Allen, regional organiser for union GMB in Nottingham, said: "Workers are worried because the writing has been on the wall at Boots for years with jobs being outsourced all the time. They are concerned about their long-term job future.
"The workers often pay the price for asset stripping that takes place by private equity firms. You wonder which companies are safe."
He said the Boots site in Nottingham was "worth a fortune" and would be an obvious target for asset stripping.
Alliance Boots is best known in the UK for its 2,600 Boots the Chemist shops on the High Street, but it also has 400 overseas outlets in countries including Thailand and Italy.
The group, which was created in a £7bn tie-up with chemist chain Alliance Unichem last year, supplies more than 125,000 pharmacies, health centres and hospitals.