If all goes to plan, Tudor will have his tour fitness test on 20 September, having already undergone microsurgery on a knee injury earlier this month.
Since then, the Surrey player has worked on his upper-body conditioning and will soon begin running following a period of rest from the operation.
Tudor provided one of brighter moments of an otherwise dismal summer for England's cricketers with his 99 not out as nightwatchman in the Edgbaston Test victory over New Zealand in July.
But his knee injury ruled him out of the remainder of the series, which became gloomier by the week in the second half of the summer - as gloomy as The Oval was yesterday, as rain washed out the first day of the county champions' final match against Yorkshire.
Medlycott said of Tudor: "He's very close now, coming along nicely, and will be fully fit.
"I expect the England and Wales Cricket Board to put together a programme for him so that he's ready for the start of the tour. It's just unfortunate that he's not going to have any bowling in match conditions.
"It's a tough job people ask these fast bowlers to do, if they can run in like a Rolls-Royce every game, then super, but it doesn't happen, or it is very seldom. We play a lot of cricket and it's important for England that they stagger their fast bowlers to keep them at their optimum."
A win or draw for Surrey will make them only the fifth side since the war to win a Championship without losing all season, something Leicestershire achieved last season.
Medlycott added: "We want to finish on a high. It's been a long, hard season and I think both sides will be feeling it."
For spectators the wet weather outside at Kennington gave all the more reason to sample the liquid refreshment on sale in the Members' bar - Surrey yesterday fixed prices at 20p a pint as they were in 1971, the year in which they last won the title.Reuse content