Negotiations to renew the deal hit a dead end and a new firm is expected to take over next year.
The BBC said it was legally required to open up the contract to outside competition and secure the best value for money for licence fee payers.
Dutch and New Zealand firms are said to be in the running for the contract, which is believed to make up a sizeable share of the 32.5 million pounds a year the Met Office receives from commercial organisations.
The Labour MP tweeted "Extremely alarmed by rumours BBC to drop UK Met Office in favour of foreign weather forecaster. Vital 90-year-old strategic relationship".
The Met Office has faced criticism of its forecasts in recent years, most notably the "barbecue summer" forecast in 2009 which preceded a washout and led the organisation to stop producing long-term outlooks.
It announced plans last year to spend 97 million pounds on a new supercomputer designed to make UK weather forecasts the most accurate in the world.
A spokesman said "Our viewers get the highest standard of weather service and that won't change. We are legally required to go through an open tender process and take forward the strongest bids to make sure we secure both the best possible service and value for money for the licence fee payer.
"Our graphics are already supplied by another provider and our long standing relationship with the Met Office will continue as we intend to still broadcast their severe weather warnings," he said.
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