The Government launched the Big Tree Plant last week to coincide with the Tree Council's national tree week, which ran from 27 November to 5 December.
"We want at least 25 hospitals to join us by March to plant trees," said a representative for NHS Forest, the group behind the project, which aims to plant 1.3 million more trees over the next five years.
The group, a coalition of experts from organisations such as Natural England and the Forestry Commission, launched the pilot project last year and is working to improve the health of staff, patients and communities through increasing access to green space on NHS land.
"We want more social cohesion between NHS sites and the local community," the representative added.
"And we want to bring together professionals and volunteers to produce woodland that includes the use of art, food crops, wood fuel and biodiversity.
"We will be working to introduce greenery to the NHS estates and planting one tree per employee, which amounts to 1.3 million trees within the next five years."