Woods has struggled with form and injury since his return to golf from personal problems, and there are now serious doubts as to whether the world number one will play in Wales when the US defend the Ryder Cup.
Montgomerie touched on Woods‘ availability for the biennial contest, saying: “It’s an unanswerable question at this stage.
“I’d like him to be in the Ryder Cup to be honest – I think any golf tournament with the world’s number one player in it is a bigger event, and if we happen to win the Ryder Cup with him playing I think it’s a better win for us.”
Meanwhile, the 46-year-old Scot is delighted with the form of his potential European players in recent months.
“I’m very happy, I must be the happiest captain in many, many years to see what’s been happening.”
He added: “The list is shaping up quite well, you’ll only know the list if all 12 are assembled at Celtic Manor, even if it’s 11 you still won’t know until I’ve got the full 12.”
The Ryder Cup begins on October 1.