The Spurs boss is just three months into an 18-month contract signed when he replaced Andre Villas-Boas, but already his position is being questioned by some as Louis van Gaal continues to be linked with a summer move to England.
Sherwood also drew criticism from some former players after publicly tearing a strip off his squad in the wake of this month's defeat at Chelsea, and there was further bad press in the week as he rowed on the touchline with Benfica counterpart Jorge Jesus.
Arsenal can stick the boot in again on Sunday and have already beaten Spurs in the FA Cup this season, but ahead of the derby Sherwood has found an ally in Wenger.
"I am always pleading for stability," he said. "Maybe you could say I'm pleading for myself. I always think technical stability is important.
"But it will become more and more difficult because in every single game there is a trial happening now on what has the manager done right and wrong. The stability will certainly be much more difficult.
"I don't know Sherwood as a coach. I knew him as a player because I am a long time in this job. I like the fact that he has learned his job and gets his chance.
"In England you rightly complain that young managers don't get a chance. When you get one you have to support him."
Wenger has seen 10 permanent Tottenham managers come and go since he arrived at Arsenal in 1996 and is expected to renew his contract beyond this summer.
By that stage the Frenchman hopes his club's nine-year wait for a trophy will be over.
He said: "Everybody at the club is focused for this game and for the end of the season to make a period where you turn your season.
"We have the strength. There are moments in a game and there moments in a season where you have to be there. With the season that we have in front of us now everyone game is a final for us.
"We are in a position where we can do well in the league, where we can do well in the FA Cup and that demands confidence and confidence is linked with results."
Watch Arsenal take on Spurs on this weekend's Super Sunday. Coverage of the day's Premier League football begins at 12.30pm on Sky Sports 1.