Wood has missed Lucknow Super Giants' last two matches due to illness but has been a revelation for them this season, taking 11 wickets in his four appearances including 5 for 14 on his debut against Delhi Capitals.
He and his wife Sarah are expecting their second child towards the end of May, and Wood will fly home at some point in the coming weeks in order to be present at the birth. At this stage, it appears unlikely that he would return to India afterwards.
England play a one-off Test against Ireland at Lord's on June 1, four days after the IPL final, but ESPNcricinfo understands that the ECB does not intend to pull players out of the tournament against their will, having previously indicated to the BCCI and to franchises that they would be available for the full season.
The ECB has actively encouraged players to travel to India to gain experience at the IPL over its last eight seasons, and the current hierarchy believe that being involved in high-stakes, knockout fixtures serves as ideal preparation for playing in semi-finals and finals of world events.
In previous seasons, the board has set a fixed return date for players involved in their first international commitments of the home summer, but they will manage them on a case-by-case basis this summer. The league phase of the IPL ends on May 21, with play-off fixtures on May 23, 24, 26 ahead of the final on May 28.
A potential early departure will depend on his own fitness, whether CSK reach the knockout stages, and whether or not he wins back his place given the success of their four incumbent overseas starters: Devon Conway, Moeen Ali, Maheesh Theekshana and Matheesha Pathirana.
The other England players likely to be involved in both the IPL and the Ireland Test are Joe Root - who is yet to feature for Rajasthan Royals - and Harry Brook, whose Sunrisers Hyderabad team appear unlikely to reach the play-offs after suffering their fifth defeat in their first seven games on Monday night.
Jofra Archer, who returned to Mumbai Indians' XI for their defeat against Punjab Kings on Saturday night, will not be rushed straight back to Test cricket after two years without playing a first-class game, though remains hopeful that he will be involved in the Ashes at some stage.