Radio Times has more info on the tender process, and what it means in this context.
Tenders are usually issued by large companies or public bodies like local authorities, and the chosen bidder gets paid to provide a specific service like recruitment or security for them.
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BBC programmes have gone out for tender before, lots of times; it just means that other production companies have a chance to take a crack at it and bring new voices to the table. It’s something they are required to do by the BBC Charter. This is also not the same thing as trying to find a streaming partner for the show.
According to the statement, the BBC will announce details of their tender process "in due course". When it’s ready it will go live on their dedicated tendering site, the BBC eSourcing Portal.
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A typical tender process starts with a tender eligibility form (TEF) so they can shortlist financially stable companies who have at least half a chance of getting something done. A full tender invitation comes to those who pass the TEF and they must sign an NDA.
Production companies will answer a series of questions like mini essays, where the question tells you exactly what they want to hear. Once the tender is submitted (usually about a month after it opens), the assessment takes between 1-3 months. The BBC will invite presentations or pitches from shortlisted bidders once the assessment ends. For a huge show like this, only a few big companies will be in the running.
Once the decision is made, all bidders are told and the standstill period begins. This is 8-10 working days and lets bidders challenge the decision if they feel it was wrong. If there are no issues, the contract can go ahead on the agreed date, and we’ll get an announcement.
It’s important to note that the BBC aren’t selling the show as part of this process. The broadcaster confirmed: "The BBC retains all IP in Doctor Who. BBC Studios will continue to lead the global distribution of Doctor Who as well as licensing, consumer products, digital and immersive experiences on behalf of the BBC."