The 31-year-old suffered the injury while playing for the Canterbury Crusaders against South Africa's Cheetahs on April 29 and had surgery. He was told he would need six weeks to recover, which would put his return date around June 10.
A test against Samoa on June 16 at Eden Park was seen as an ideal way for Read to get some match fitness before the Lions series but he said on Thursday the longer he had on the sidelines, the better.
"At the moment they are kind of saying you can't use it for six weeks, which is a week before the Samoa game," Read told New Zealand's Radio Sport. "We'll just have to see if I push it, or let things go before that first test (against the Lions).
"It's the type of injury where you can push it if you want to, but that increases the risk of a re-break.
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"They say that six weeks is a bit of risk, seven weeks is only a slight risk, eight weeks you are pretty much sweet. The (risk) decreases pretty quickly. It's just a matter of how you want to operate."
Read, who also missed the first six weeks of Super Rugby as he recovered from wrist surgery, said he was still training while protecting his thumb and was not fazed about a lack of match fitness for the series-opener in Auckland against Warren Gatland's team.
"In terms of match fitness I won't have too much, to be honest, going into that first test but I've done this gig a few times," he added.
"I've got the confidence in myself that I can turn up and play at a high level. I'll back myself and I'll be good, ready to go."
(Reporting by Greg Stutchbury; Editing by Ian Ransom)
