Tottenham, who sacked manager Andre Villas-Boas on Monday following a humiliating 5-0 home Premier League loss to Liverpool, are yet to meet with former midfielder Sherwood to discuss his ongoing role.
"I got a call at 10:15 on Monday from the chairman asking me to take the first team training but the immediate future beyond that is up in the air," Sherwood, who was an animated figure in the technical area during the game, said.
"I'll have to have a chat with the chairman. There are lot of big names being bandied about as you would expect because it's a huge club but the chairman needs to make the right decision and find the manager that is compatible to take this club forward."
Asked if he wanted the job, Sherwood, who has been in charge of the development squad, said: "It would have to be right for me and right for the football club."
He was not sure if he would be in charge for Tottenham's trip to Southampton on Sunday.
With their season coming apart at the seams, however, Sherwood feels a decision should be made soon.
"Confidence has taken a battering and whoever is in charge on Sunday and for training on Friday needs to get the team prepared. If it's me I won't go in all doom and gloom.
"I haven't spoken to the chairman but it would be good to get it resolved for the club. I'm in the frame but it's not my decision unfortunately."
It is the season of goodwill, but charity was in short supply as West Ham fans mockingly chanted, "You're getting sacked in the morning" at Sherwood as the final whistle sounded.
"I'm not used to sleeping two hours a night thinking about football players," Sherwood, a Premier League winner with Blackburn Rovers, said of his sudden elevation.
"It's madness, isn't it really? But I've always been up for a challenge."
From the meticulous build-up play under Villas-Boas, Tottenham were far more energetic in the opening 20 minutes against their London rivals, carving out several chances.
When Emmanuel Adebayor, brought in for his first start of the season by Sherwood, finally opened the scoring with little more than 20 minutes remaining it seemed the rookie manager would enjoy a dream night.
However, West Ham hit back with goals by Matt Jarvis and Modibo Maiga to send Spurs fans trudging away into the north London rain.
"We ran out of steam," Sherwood said.
"They are fit enough to play a certain way but I wanted to change the way we played. It's a complete change of mindset. I wanted a bit more gung-ho and up-and-at-them but you need to acclimatise for that."
Despite being five points off the top four in the Premier League, there is a sense of despondency pervading the club.
The optimism with which they began the campaign after spending more than £100 million on seven players, albeit money recouped by selling Gareth Bale to Real Madrid, has long since disappeared.