"The silence is deafening, isn't it?" Sherwood was quoted as saying by British media on Monday.
"It's up to Daniel. I didn't know if he was at the game or not. Maybe he was travelling."
Former Barcelona and Bayern Munich coach Van Gaal said in an interview with Spanish sports daily Marca on Saturday he was interested in a move to England to round off his career and acknowledged the Spurs link.
His appointment would be the high-profile name fans were seeking in December following the sacking of Andre Villas-Boas.
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Instead, Sherwood was surprisingly handed the job and then an 18-month contract after stepping up from his role in charge of the development squad.
The former Spurs and Blackburn Rovers midfielder was previously an assistant coach at the club under former boss Harry Redknapp but said he had no plans to resume the role if Van Gaal took charge at White Hart Lane.
"I feel I can do the number one job but I'd be no good as a number two, I'm too opinionated. I wouldn't want to do the job," the 45-year-old said.
"There is a place for a technical director, someone who sees the club from bottom to top of the training field.
"There's a definite place for that, otherwise you get no continuity and end up buying seven or 10 players every window and your turnover of players is too great."
Italian Franco Baldini currently holds the technical director role at Spurs but British media reported his position could also be in jeopardy after a season that promised so much has produced a number of lows.
Baldini helped Spurs sign seven new recruits at the start of the season at a cost of over 100 million pounds ($167.21 million) but Erik Lamela and Roberto Soldado in particular have struggled. Three of the seven started on the bench against Chelsea with the other four injured.
HURTING
Tottenham's season unravelled when a 5-0 home loss to Liverpool, which followed a 6-1 defeat at Manchester City, proved the end for Villas Boas and while Sherwood has brought some positive form, his reign has also seen similarly large defeats.
Beaten 5-1 at home by City in January, they fell apart in a 4-0 loss at Stamford Bridge on Saturday after being level with just over 30 minutes remaining.
"We lack something don't we?" the manager said. "Capitulations are happening too often.
"In adversity, when things go against us, that's when we go missing. You either have that in you or you haven't. We need to stand up and be counted sooner rather than later.
"One thing I guarantee is that no one cares more than me. I want the team to do very well and it hurts me when they don't. I'm afraid I need people in that dressing room to be hurting like I am."
Spurs are fifth on 53 points, four points behind City who are in the fourth and final Champions League spot but have three games in hand on the Londoners.
"Slim" was how Sherwood described the prospects of qualifying for the lucrative European competition next season with nine league games remaining starting with Sunday's clash at home to bitter north-London rivals Arsenal.
Before that, Spurs host Benfica in the first leg of the Europa League last 16 on Thursday with injury doubts over club captain Michael Dawson, who limped off against Chelsea with a hamstring injury.
Samuel Eto'o put Chelsea in front before winning a penalty that resulted in a red card for Younes Kaboul, whose suspension leaves Sherwood with a defensive headache. Eden Hazard converted the spot kick before Demba Ba added two late goals in the rout.
"The fans were magnificent and the lads owe it to them and owe it to themselves," Sherwood said of the need to respond in the next two games.
"They have to take it on the chin, as we all have."
($1 = 0.5981 British Pounds)
(Writing by Patrick Johnston; Editing by Greg Stutchbury)
