Tiger Woods believes he should be at this year's Ryder Cup — but accepts he may have to do more to convince United States captain Tom Watson.

Former world number one Woods is on the comeback trail after a three-month lay-off following a back operation.

Woods’s appearance at the Open at Hoylake this week was just his second since undergoing surgery in March. After playing all four rounds at Royal Liverpool, Woods appears to have proved his fitness but his form is a different matter.

The 14-time major winner had mixed fortunes on the Merseyside links, finishing six over after a three-under-par first-round 69 and a final round of 75. Having fallen well down the standings for automatic Gleneagles selection during his absence, he may be relying on being named as one of Watson’s wildcard picks for the September match.

Asked if he should be selected, Woods said: “I would say yes, but that’s my position, my take on it. He’s the captain, obviously it’s his decision. He’s going to field the best 12 players that he thinks will win the cup back, and I hope I’m on that team.”

Woods has been a wildcard pick before, in 2010 when Corey Pavin added him to his side for the competition at Celtic Manor.

The 38-year-old said: “I got picked by Corey back in whenever it was when we played in Wales. I was coming off an injury as well there with my Achilles, and I sat out for most of the summer.

“I felt like I was able to contribute to the team and that’s all you want as a pick, you want someone who can contribute to the team, whether it’s in support or it’s in play.

“I did it then and hopefully I can actually earn my way on to this team.”

Woods is confident he can do that in the most convincing fashion with outstanding performances in the coming weeks at the Bridgestone Invitational - which he won last year - and the US PGA Championship at Valhalla.

He said: “Well, I’d like to win the next two tournaments I’m in. That should take care of that.”

Woods’s final round at Hoylake included a double-bogey six at the seventh hole and four other bogeys.

Assessing his week on the Wirral, he said: “I got four rounds in, unfortunately I didn’t play very well today. It was a little different on the first day, obviously, but I just made too many mistakes. I had two triples (bogeys), two doubles. Just way too many mistakes.

“But the fact I was able to play a few weeks ahead of time, and I’m only getting stronger and faster, is great.”

Woods, a triple Open champion, finished five strokes behind 64-year-old five-time winner Watson, who closed with an impressive 68. Watson has said he will pick Woods for Gleneagles if form and fitness warrants it, but will make no guarantees if he fails to make the play-offs for the FedEx Cup.

Watson had hoped to speak to Woods at some stage during their week at the Open but that has not occurred. He said: “I just said hello. We’re going to talk on the phone. But it’s a little bit early with Tiger to even talk to as far as where he is. Where it needs to be is higher up on the list.

“It looks like he’s playing without pain but, again, he’s not in the mix. He needed to get in the mix to get some points to get some money and get in the FedExCup. That’s what I was hoping he was doing this week.”

Phil Mickelson is another high-profile American player currently outside automatic selection. Watson said: "If Phil and Tiger don't make it in the mix there, I've got some real thinking to do. Everybody is thinking that I'm going to pick them automatically but I can assure you that I'm not going to pick them automatically."