Khan had been playing for Surrey instead of the injured Saqlain Mushtaq, but then had to join India's Asia Cup squad.
A Surrey spokesman told BBC Sport the club was hoping to tie up a deal soon.
He said: "Brett Lee is one of two players we are considering. If we can get Lee he will be a useful addition to our bowling attack."
Lee is looking to spend some time in English County cricket in an attempt to prove his fitness ahead of Australia's tour to India in October.
He has been out of action since suffering an ankle injury during a tour to Sri Lanka four months ago.
But he has been bowling in the nets and is due to spend some time in India working with Test legend Dennis Lillee.
Another Australian, batsman Greg Blewett, was signed on a short-term contract by Surrey as cover for the injured Azhar Mahmood but he is expected to return to action next week.