Prior experienced some mild tightness in his right thigh during training yesterday and England have called up uncapped Lancashire gloveman Jos Buttler as precautionary cover.
However, Prior looks set to play in the match which starts tomorrow.
Cook said: "We're 99 per cent certain that he'll be fine.
"Of course, we'll have a little check in the morning just to make sure, but all things at the moment look good."
He added: “It was a bit of a concern yesterday with his thigh but he's done everything we've asked of him today, and looks really good. Fingers crossed, he should be alright.”
While Prior’s fitness represents one poser for Cook and Head Coach Peter Moores, another is the make-up of the rest of the XI.
Fit-again Ben Stokes, England’s star of the winter Ashes campaign, has been added to the squad that faced Sri Lanka last month.
If he plays, someone who impressed against Angelo Mathews’ side will have to make way.
“It’s a tough selection call and that’s what you want as a captain and as a coach of a team,” Cook added of Stokes’ return to the squad.
“For a guy who’s been out injured, he’s come back, he’s got 10 wickets for Durham (versus Sussex in the LV= County Championship two weeks ago) and his previous record for those four Test matches in a tough situation in Australia, he was the standout player. And then you’ve got other people who’ve done well in his absence.”
India have warmed up for the five-game series with a draw against Leicestershire and victory over Derbyshire, both matches without first-class status given the tourists’ use of more than 11 players in each.
India’s seamers, led by Ishant Sharma, will be key to prospects of taking 20 wickets in a Test, something the tourists did just once when they were whitewashed 4-0 here in 2011.
Skipper Mahendra Singh Dhoni said: “We have had some time to adjust to the conditions.
“We have done a lot for the fitness of the fast bowlers. We have worked really hard in the last 10-12 days. Now we are going through a period where we are easing the workload of the fast bowlers.
“I think in the practice sessions whatever we have had so far, I think they’re bowling the right lengths; they’re making the batsmen play which is very crucial in these conditions.
“Overall as a bowling unit they are looking very good and hopefully we won’t have injuries and we’ll move forward in the right direction.”
Investec Test facts
The only other time England hosted India in a five-match Test series they won 5-0, in 1959.
The three leading run-scorers in England v India Tests in England are Indian (Sachin Tendulkar, Rahul Dravid and Sunil Gavaskar).
Ian Bell has scored 428 runs in his last three Test innings against India in England.
James Anderson (225) needs five wickets to pass Fred Trueman (229) as the leading Test wicket-taker in England. Ian Botham has 226.
In the last series between these teams in England, in 2011, the hosts recorded their largest home run-margin victory against India – they won by 319 runs at Trent Bridge.
Stuart Broad took a hat-trick in that match. He recently became the only England bowler to take two Test hat-tricks when he repeated the feat against Sri Lanka at Headingley.
In the 2011 series England hit seven centuries to India’s three – all of which were recorded by Dravid.
Matt Prior (29) is the wicketkeeper with most dismissals in England v India Tests in England.
Since the start of the 2007 series, England have recorded 14 century partnerships to India’s four in Tests between these teams in England.
Broad’s bowling average of 13.8 at home against India is his lowest against any team on home soil.
Dilip Vengsarkar has hit three centuries at Lord’s. He is the only overseas player to record more than two at the venue.
Tendulkar is the leading run-scorer in Tests between England and India in England (1,575 at an average of 54.3).
Kapil Dev is the only player to score 5,000 runs and take 400 wickets in Tests.
Mahendra Singh Dhoni has led India 53 times in Tests, more than any other Indian. Eight players have captained their teams more in Tests.