Earlier this season the 40-year-old Hick became only the second player since World War II, after Yorkshire great Geoffrey Boycott, to score a hundred first-class hundreds for a single county and only the eighth player in all to achieve the feat.
Worcestershire chief executive Mark Newton said the club had no qualms about offering Hick, whose present deal expires at the end of the current campaign, a contract for what would be a 24th season of county cricket.
"Graeme is a legend of Worcestershire cricket and is having another good season," Newton explained.
I can confirm we recently discussed the situation with him and would love to see him continue to re-write the record books here at Worcestershire.
"The offer has been made and Graeme has asked for time to consider the situation," he added.
Hick's 139 against Northamptonshire in June, as well as being his hundredth hundred for Worcestershire, was the 130th first-class century of his career.
It left him in eighth place in the all-time lost of first-class centurions.
But unlike many players with a similarly glittering record in the county game Hick, born in what was then Rhodesia and now Zimbabwe, did not enjoy a highly successful Test career.
He was forced to serve a residential qualification period before making his England debut in 1991.
Repeatedly dropped and recalled by England, he was famously labelled "a flat-track bully" by New Zealand coach John Bracewell.
Hick played the last of his 65 Tests against Sri Lanka at Kandy in 2001, finishing with 3,383 runs at a modest average of 31.32 with six hundreds.
But his first-class record will be tough for any contemporary or future player to top.
Since Hick made his Worcestershire debut in 1984, there has been a huge reduction in the number of first-class fixtures.
Meanwhile the accompanying growth in the Test programme has led to England batsmen making fewer and fewer appearances for their counties, with the national team management increasingly ordering to them rest between international matches.