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Vettori has not played for the Black Caps for almost a year because of a hamstring injury and was left out of the squad for the two-Test series in England.
But with Martin sidelined by the injury that prevented him bowling during England's second innings of the first Test, which ended with a 170-run win for the hosts at Lord's on Sunday, there is a vacancy for a spinner heading into the second Test starting in Leeds on Friday.
Vettori, named in New Zealand's squad for their one-day internationals against England and next month's Champions Trophy, is due to link up with the squad on Tuesday.
And the former New Zealand captain could come into the reckoning as a replacement for Martin at Headingley.
"Daniel's come over 24 hours earlier for us to have a chance to have a look at him," New Zealand coach Mike Hesson said on Monday.
"We won't risk Dan for the sake of a Test but, in saying that, it is an important Test match for us.
"We won't be pushing Dan if he's not ready but if he is we'd certainly love to have him."
With 360 victims to his name, left-arm spinner Vettori is New Zealand's second highest Test wicket-taker.
His last Test was a nine-wicket defeat by West Indies in Antigua last July and his only international action since then was at the World Twenty20 in October.
The only other bowling option open to McCullum is seamer Doug Bracewell, who was left out of the first Test.
