Root, England's Test captain, has never been picked up by an IPL franchise and has not entered the auction since going unsold in 2018. The ECB is yet to confirm the centrally contracted players' availability for the 2022 edition, but with England's first Test against New Zealand starting on June 2, Root would likely be required to leave the IPL before the knockout stages if picked up.
Wood has played in the IPL before, appearing for Chennai Super Kings in 2018, but withdrew from last year's auction at the 11th hour in order to spend time with his young family.
Both players said this week that they were interested in the prospect of playing in the IPL - Wood has already submitted his paperwork for the auction - but that they would only do so if taking part does not detract from their Test commitments.
"I have not made a decision on the IPL just yet," Root said on Wednesday. "It is something I will have to keep wrestling with. Time is ticking but I have a lot to weigh up. The thing I will weigh up is: will it have a negative impact on me playing Test cricket for this team? If I don't think it will, then I will put myself in that position to play and put myself in the auction.
"But I will never compromise or do anything that will detract from playing Test cricket for England. It is so important to make sure that is the priority for me and other players as well."
"We've seen the benefits to other fast bowlers. I was watching [Anrich] Nortje do well there. When we played the T20 competition [World Cup] he looked really good because he's had that experience"Mark Wood
There is no guarantee that Root would get a deal if he put his name forward. He has not played a T20I since May 2019 and his England commitments in Test and ODI cricket have limited his availability for domestic T20 cricket: he made only six appearances in the T20 Blast between 2013 and 2019, and had a quiet short-form season in 2021, making 97 runs across six games for Yorkshire and Trent Rockets.
Wood is more likely to pick up a contract. Overseas fast bowlers have been valuable assets for IPL franchises in recent years, and he attracted interest from Mumbai Indians before the postponed 2020 season as a potential replacement for Lasith Malinga.
Wood has entered the auction at the highest base price, INR 2 crore (US$ 269,550 approx.) but said that the chance to improve as a T20 bowler ahead of another World Cup in Australia next year was more important than any prospective financial rewards.
"There's a World Cup at the end of the year I have my eyes on," Wood, who turned 32 on Tuesday, said. "It hurt a lot this winter when we got knocked out in the [T20 World Cup] semi-final [by New Zealand] and it feels as a one-day group that it's time to push hard to leave a legacy behind.
"At the minute, I'll be in it," Wood told reporters in Hobart on Thursday. "But it's important to have that time at home and reflect. It's just whether the time away from home, the bubbles… I've done Australia without my son (around), which has been quite hard, especially around Christmas, so I'll have to see how the family situation is.
"If I look ahead to the World Cup and I can learn something in the IPL, if I can put myself in pressure situations and try and get better for the end of the year, that'll be good. We've a really good one-day team and this could be our time to really win things. That's a burning desire.
"From a financial side of things, it's great to go in, but actually the reason is cricketing, because of what's to come with England. I just felt the reason I'd have gone last year was purely financial; this year, it would be about trying to improve and put myself in those pressure situations for later.
"We've seen the benefits to other fast bowlers. I was watching [Anrich] Nortje do well there. When we played the T20 competition [World Cup], he looked really good because he's had that experience. If I can move my game forward that would be brilliant."
Matt Roller is an assistant editor at ESPNcricinfo. @mroller98