The museum is currently looking at PR support for a project brief to begin in the summer and last beyond Christmas.
The winning agency, which will also work with the National Railway Museum and National Media Museum to promote their gift items, will report to John Barford, head of retail at the Science Museum.
Andrea Dearden, head of marketing and PR at the Science Museum, said the tender had closed, with a decision expected to be made shortly.
It is the second year that the museum group has brought in outside help, with The Press Office handling activities previously.
Dearden said: 'We have a wide range of products at the Science Museum, many of which you would not necessarily think we would have.
'Whether it's rubbers for youngsters or microscopes, we have much to offer.
We are also looking to develop our adult range, which includes recyclable jewellery. This is about spreading awareness and Christmas will be a really important time for us.'
The Science Museum is currently working with Forster PR on a climate change programme.