The Liberal Democrats have made the authority which was once led by the Education Secretary, now the Sheffield Brightside MP , their top target.
They currently hold 36 out of the 87 seats, 14 less than Labour. Howard Sykes, chief executive of the Association of Liberal Democrat councillors, said: "We are very optimistic of taking control."
Their belief is shared by local government analysts who expect Labour to lose Sheffield along with Kirklees, where there are seven Conservative councillors, 43 Labour, 30 Lib Dems and two others.
Another key battleground will be Herefordshire, where Labour could lose control in five of the six district councils it holds.
Labour is also worried about the Liberal Democrat advance in Bristol and could be deprived of its overall majority in Milton Keynes, North-east Lincolnshire and York.
The Liberal Democrats run 13 local education authorities - controlling 11 outright.
Mr Sykes said: "It would be a major achievement to take Sheffield and it will be pretty embarrassing to Mr Blunkett. People are interested in education. There is some evidence that national government is delivering on class sizes for children aged five to seven but the consequences are that those for eight to 11-year-olds are rising.
"Two years on people are starting to ask 'Those Portakabins we've had for 30 years, are they being replaced?' The answer is no."
More than 13,000 seats in 362 councils in England, Scotland and Wales are being contested in the local elections on May 6.
All district councils, English shire unitaries and Welsh unitaries will be holding elections. The London boroughs will not be taking part - their next elections are May 2002. The county councils will hold elections in 2001.
Hilary Armstrong, the local government minister, admitted this week that the party was expecting to lose up to 1,500 seats across the country. She said Labour would suffer more than any other party as it was defending its best ever local election results. It won 47 per cent of the vote in 1995, the last time 13,000 seats in England, Scotland and Wales were contested.
Meanwhile the Tories, who had originally hoped to gain between 700 and 800 seats, have now revised their target to "below 400".
They are on course to win seats from Labour in the south and are also tipped to take Bromsgrove.