UPDATE: 'Canes captain seeks NZ release to face Boks
The highly-rated flank is heading to Premiership side Wasps at the end of the Super Rugby season after giving up on All Black selection.
Kiwi-born but eligible for England through his parents, the 27-year-old was expected to feature in coach Eddie Jones' plans for the 2019 World Cup.
But it appears Shields' chance may come sooner than initially expected, with reports in Britain saying Jones wants him in the England squad to tour South Africa in June.
The England coach is attempting to get his side back to winning ways after an underwhelming defence of their Six Nations crown which saw them lose three successive matches.
Shields has led the Hurricanes to the top of the Super Rugby standings and his physical presence would be an asset for England against the Springboks.
However, his contract with the Hurricanes runs until the end of the Super Rugby season in August, meaning he needs permission from New Zealand Rugby.
"We're looking at it and considering the ramifications of releasing him to play for England in the middle of a competition that he's committed to," Tew told reporters.
NZR would not normally be expected to do England any favours, particularly since the All Blacks will meet Jones' team in November.
But Shields is a widely-respected figure in New Zealand – regarded by many as unlucky to miss All Black selection – and Tew said this would be considered in NZR's deliberations.
"There's no point not acknowledging that Brad's been a very good servant of the game for a long period of time," he said.
"He's asked for some dispensation and we'll give that serious consideration."
If NZR refuse to release Shields, England could take the matter to arbitration before World Rugby.