Sherwood's position at White Hart Lane has been the subject of speculation ever since he replaced Andre Villas-Boas in December, despite a record of 12 wins from 20 games making him, statistically, the club's most successful boss in the Premier League era.
A contract which runs until next summer seems to mean very little to the Spurs board, who are believed to have already made up their mind that another fresh face is needed at the end of the season.
Tottenham have described this report as "wholly inaccurate", but do seem to maintain an interest in former Barcelona defender De Boer, who turned down the chance to succeed Villas-Boas in the New Year.
Meanwhile, rumours are suggesting that Allardyce, who was appointed Hammers manager in June 2011, could be axed if they suffer defeat in the London derby at Upton Park this weekend.
The 59-year-old has virtually guided the Irons to top-flight safety, with five points separating them and the relegation zone with two games of the campaign remaining, but a run of four straight defeats and complaints over his unattractive and direct playing style has seen the pressure on his job resurface.
Joey O'Brien has resumed training following a dislocated shoulder, but is unlikely to be rushed back with so little to play for between now and May 11. Marco Boriello completes West Ham's injury list.
After missing the loss to the Baggies due to personal reasons, Matt Taylor is available again, but will probably only be named on the bench alongside Joe Cole, who appears poised to leave the club for a second time.
Kyle Walker, a regular for the Three Lions during qualifying, is also a doubt for Roy Hodgson's squad for the tournament in Brazil, with his hip concern likely to keep him out for at least another month.
West Ham: LLLLWW
Possible starting lineups
West Ham: Adrian; Demel, Collins, Reid; Armero; Noble, Nocerino, Nolan; Jarvis, Downing; Carroll
Spurs: Lloris; Naughton, Dawson, Kaboul, Rose; Lennon, Paulinho, Chadli, Eriksen; Adebayor, Kane
Sports Mole says: 1-1