Close, which has no stake in Jarvis, wanted to replace chief executive Kevin Hyde and acting finance director Alistair Rae with a temporary "boarding party". Norris has rejected the proposals.
Jarvis shareholders claim that Close stood to gain if the new team decided to break up the group in some way, in which case Close's consultancy talents could be employed.
One said: "It could be thought that Close would only put in management that it thinks will give them advisory work. It is in Close's interest for a new team to make certain transactions, but these transactions may not be in the best interests of the shareholders." The shareholder said the situation would be different if Close had taken a stake in the company.
City analysts agreed. One said: "It does all seem odd. Vested interest was definitely a thought that crossed my mind."
A Jarvis spokesperson said: "Close is not a shareholder. Its approach has not gained any credibility with the chairman and board of Jarvis."
Shareholders have also expressed concern about the fact that Close wanted to replace Rae, who is preparing a strategic review of the business. Rae is viewed as an independent figure untainted by the problems that have affected the firm, and many want to see what his proposals are.
Close Brothers declined to comment.