Ashley Giles's lengthy absence because of a hip injury has given Northamptonshire left-armer Panesar a chance to show what he can do in international cricket.
So far the 24-year-old, the first Sikh to play for England, has made an encouraging start to his Test career with 25 wickets in his first eight matches including a superb match-winning return of five for 72 in the side's crushing innings and 120 run victory over Pakistan in the second Test.
Panesar's return at Old Trafford on Saturday, where England won inside three days to go 1-0 up in the four-match series, was especially impressive as he dismissed five of Pakistan's top six including the 'big three' of captain Inzamam-ul-Haq, Younis Khan and Mohammad Yousuf - all noted players of spin.
His attacking style has led many to suggest that Panesar should retain his place even if the more defensively-minded Giles, a valuable member of England's Ashes-winning team last year, regains full fitness.
But Fletcher said Panesar had to improve his batting and fielding, the latter a particular concern, to secure his place in the England team.
"I think Monty is a very good bowler, but we have to produce 11 players who can produce two of the departments efficiently, whoever is playing for England," said Fletcher.
"I still have slight reservations about his batting and his fielding, but he's an outstanding bowler and doing a job for us because there's no-one else at the moment who can fulfil that role.
"He needs to work hard at it because if you work hard at your fielding you can really improve that a great deal. It's not easy to turn you into a No. 6 batter, but I just think you need to work at those two areas."
Giles, capable of taking some sharp catches in the gully, had developed into a handy lower order batsman with an average in excess of 20 and, asked who was now England's leading spinner, Fletcher said: "It will depend on when Ashley is going to be ready and how Monty bowls on other wickets and we'll have to make a decision when Giles is ready.
"We'll also have to look at the balance of the side. It was a good wicket for Monty to bowl on and he bowled damn well on it, but we've got to make sure in the future we get wickets that help our bowlers like that.
"Quite often when you get onto a wicket like that you can try too hard because you know it all depends on you, but he went out there and bowled a good line and length and spun the ball on occasions a great deal."
Meanwhile Giles, speaking on BBC Radio's Sportsweek programme, admitted he had a fight on his hands.
"Monty is the man in possession and I have to get my place back - that's the danger if you do get injured.
"My recovery is going okay, it is just frustrating.
"I cannot bowl and cannot run but the rehab is going well. It is going to be another four or five weeks until we reach that point."
Giles also paid a generous tribute to Panesar, saying: "Monty is a brilliant technician and works extremely hard. He is able to land the ball in good areas and put batsmen under pressure."
England are due to announce their squad for the third Test at Headingley later Monday where victory, in a match starting Friday, would see England take an unbeatable 2-0 lead after the drawn series opener at Lord's.
However, wicket-keeper Geraint Jones - who took the field at Old Trafford despite a fractured right ring finger - remains doubtful and his longstanding rival Chris Read, who played for England A against Pakistan earlier this season, could be called in as cover.