I'd be uncomfortable about a tree that close to the house unless I knew precisely which variety it was and it was a small tree, say no more than 4 metres tall with a similar spread. Even that means branches may later scrape against the upper parts of the house though. I note that the tree is tending to lean away from the house already, in an attempt to head for more light. Willows in particular do like a lot of water, and have a tendency to infiltrate any sources of water such as drains and pipes, especially if drought occurs regularly.
In terms of subsidence or a threat to the house foundations, that's usually only a major threat on clay soils, but I wouldn't plant any Willow within 12 metres of a structure with foundations of any sort, even on non clay soil. Some more reading here which might help you decide https://www.rhs.org.uk/advice/profile?pid=225 but otherwise, consult a reliable tree surgeon or arborist for their opinion.
You've said your soil is clay, which means I'd recommend removing it - if you want something there to replace it, a taller shrub/small tree such as one of the Amelanchiers would be safer. Amelanchier 'Obelisk' for instance is quite narrow and won't be bumping into the upper parts of the house, but note that Amelanchier does not like limy soil.