The Sussex paceman, 25, won the man-of-the-match award on two occasions in the one-day series against Sri Lanka.
Asked who might be in the squad, skipper Alastair Cook said: "CJ has done everything asked of him and given a massive nudge to the selectors."
Lord's hosts the first Test on 12 June, followed by Headingley on 20 June.
Key selections for England surround an opening partner for Cook, a wicketkeeper and a spinner.
12 June: 1st Test v Sri Lanka, Lord's
20 June: 2nd Test v Sri Lanka, Headingley
9 July: 1st Test v India, Trent Bridge
17 July: 2nd Test v India, Lord's
27 July: 3rd Test v India, Southampton
7 August: 4th Test v India, Old Trafford
15 August: 5th Test v India, The Oval
Jordan has impressed with bat and ball in one-day internationals since making his debut in the home series against Australia last year.He hit 38 from 13 balls and took 3-25 in the first match against Sri Lanka at The Oval and returned the best figures by an England bowler at Old Trafford with 5-29 in match three.
Regular wicketkeeper Matt Prior was back behind the stumps for Sussex on Sunday following Achilles trouble, and his county coach Mark Robinson says he ready to play.
"The Achilles problem is not going to go away until the end of the year but it is manageable. He is ready mentally," Robinson told BBC Radio 5 live.
"With the bat he's in form. What he has not been able to do is keep wicket, so he might be slightly undercooked but in this game, he has improved.
"If I were Alastair Cook or Peter Moores, I would want him in my side."
There have been calls for one-day wicketkeeper Jos Buttler to be elevated to the Test team, but they were played down by Cook recently.
Buttler struck the fastest ODI century by an England batsman during the Sri Lanka series but Cook is yet to be convinced he is ready.
In their most recent Test campaign, England used 18 players during the disastrous 5-0 defeat against Australia in the Ashes last winter.
Discarded former England batsman Kevin Pietersen on Twitter: "England selectors meeting today...I'm ready to go! Fancy Lord's next week...I'm a number 4 batter & bowl off spin."
First-choice spinner Graeme Swann retired midway through that series, number three Jonathan Trott has only recently returned from another break to address stress-related issues and premier batsman Kevin Pietersen has been discarded from the set-up following conflict with the England hierarchy.Michael Carberry opened the batting with Cook in all five Ashes Tests last winter, scoring 281 runs in 10 innings with a top score of 60.
The 33-year-old Hampshire left-hander averages 42.50 from five matches in Division Two this season with a best of 100, however he could face competition for his place from Middlesex's Sam Robson.
The selectors - James Whittaker, Angus Fraser, Mick Newell and coach Peter Moores - may decide Joe Root's part-time off-spin is sufficient in what are expected to be seam-friendly conditions.
Should they decide that is the case, Worcestershire's Moeen Ali, who can bat in the top six and also bowl off spin, could also come into contention.
Promising all-rounder Ben Stokes, who topped the England batting averages in the Ashes and was the only player to score a century, has also recently returned from a broken hand.