The New Zealand team arrived in Southampton on Tuesday for the inaugural World Test Championship final, starting June 18 at the Ageas Bowl.
If all goes well, the South Africa-born Wagner, who is No 4 in the ICC Test rankings, should be lining up for his adopted country in the final of the World Test Championship.
India vs New Zealand WTC Final: I will be looking forward to Trent Boult vs Rohit Sharma contest, says Virender Sehwag
Virender Sehwag feels opener Rohit Sharma countering Trent Boult's incoming deliveries will make for a fascinating contest.
England's Ollie Robinson was suspended after racist and sexist tweets posted by the paceman in 2012 and 2013 emerged during the first Test at Lord's.
New Zealand coach Gary Stead also informed that left arm seamer Trent Boult is available for the second Test, while one of the fast bowlers will be rested for the Birmingham game.
Boult, who has snared 281 wickets in 71 Test, will be unavailable for the first Test as he has opted to spend time with his family after the suspension of the IPL mid-season.
New Zealand pacer Trent Boult on Sunday said that India has given him so much both as a cricketer and a person.
Mumbai Indians pacer Trent Boult on Thursday said that 'Mankading' still remains a sensitive issue in the sport.
Strength of Mumbai Indians is to fight till the end, bowlers looking to adapt to the dew: Trent Boult
Mumbai Indians middle-order has struggled in all four games and the side has failed to post a total in the range of 170-180 even once.
Bumrah bowled economically and just gave 14 runs in his fours overs including a wicket while Boult returned with the figures of 3-28.
Back at the top with his opening partner Warner, Bairstow amassed 18 runs from Trent Boult in the third over with the help of three fours and a six.
Besides the 36-year-old Taylor's absence, fast bowler Lockie Ferguson, who suffered a bone stress injury in his back, was also left out from the squad for the three-match series.
Boult said he has been struggling to forget the 49th over in which he took a catch of Ben Stokes off Jimmy Neesham but ended up stepping on the boundary to let the advantage slip.
New Zealand declared their second innings at 291 for eight, with Taylor 107 not out, and then took two top-order wickets by stumps.
The new ball pair then took four wickets between them on a benign pitch as the West Indies plummeted to 215 for eight at stumps.