The Spain international arrived to much fanfare in a B£26million summer deal, but has so far failed to live up to the billing.
Soldado's struggles saw him go two months without a goal before last weekend, when he netted his first in nine games as Tottenham beat Cardiff 1-0.
The relief was palpable and fans' favourite Chivers - a man who bagged 174 goals in 367 games for the north Londoners - is confident the Spaniard can still be a success at White Hart Lane, if he gets the right service.
"Tim Sherwood has certainly done well with Emmanuel Adebayor to give him the confidence and make him grow happy enough to show us what he can do," he told Press Association Sport.
"He has persevered with Soldado and I feel very sorry for him as you can't play him in every game when he is missing goals galore.
"But we know than he can score goals - you don't suddenly become a bad player, but you have to have the service and I don't think we create that many chances."
The air of relief following's Soldado strike against Cardiff was highlighted by the manner in which the team celebrated en masse with the forward.
Chivers believes that moment captured the camaraderie cultivated by Sherwood, who he hopes is given a chance to make his mark on the job amidst talk of a summer departure.
"I think the team spirit is very good under Tim Sherwood," he said, speaking at the Football Legends Awards in aid of the Willow Foundation, which supports seriously ill 16-to-40-year-olds.
"I have been working there for 24 years now and seen 14 managers come through. That is not conducive to success and I don't want to see a 15th manager soon.
"It is up to the club and the way they are thinking, but I am sure if Tim Sherwood gets good results before the end of the season, even if we just miss out on the Champions League, he has a very good chance to carry us on."
Spurs face a vital trip to Chelsea on Saturday before facing Benfica in the Europa League last 16 next week - a match they go into without their top continental scorer, Jermain Defoe.
The 31-year-old England international netted five goals in the competition this season - which saw him overtake Chivers as Spurs' all-time top goalscorer in Europe - but has now moved on to Major League Soccer side Toronto FC.
"We needed a Jermain at the football club but he has been offered something he can't turn down at his age," Chivers said.
"He has got a gold mine, struck lucky. I just hope he can go through the five years because he will be set for life. I am pleased for him.
"Jermain has given us some fantastic years, he has scored many goals but I think he needs another challenge and I think that challenge over there is just right at his age."
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- Tim Sherwood