Tudor, who missed the second and third Tests due to a knee injury, is expected to have recovered by the start of the match at The Oval on August 19.
But he will be short of match practice, and England selectors will have to decide whether to gamble on Tudor on his home ground.
He was the hero of the first Test at Edgbaston, when he hit 99 with the bat to help England to an unlikely victory.
Surrey coach Keith Medlycott said: "He will probably be fit but whether he will have played enough cricket by then is another question.
"We have been keeping close tabs on him and he is going along nicely but we don't want to rush him back.
"He will be seeing a specialist tomorrow and if he thinks there's any doubt we won't rush him back into the team."
England's Tudor rose
(03 Jul 99 | England v New Zealand)
Tudor crowned King of the crease
(03 Jul 99 | England v New Zealand)
NZ struggle as Tudor shines
(03 Jul 99 | England v New Zealand)
Official player ratings
Lord's
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