The speculation followed public criticism of its treatment of subcontractors and delivery of school projects. All the allegations have been strongly denied by the firm.
Jarvis also issued a profit warning last Wednesday when it said that year-end profitability would be £12m lower than expected. Jarvis blamed this on delays that have hit 14 PFI schemes.
A Jarvis spokesperson denied that Hyde, who succeeded Paris Moayedi as chief executive last May, was about to leave.
He said: "There is absolutely no question of Kevin Hyde leaving his position as group chief executive of Jarvis. Kevin is committed to seeing through his strategy for Jarvis and moving the company forward in its chosen markets of infrastructure services and facilities management."
A source close to the firm claimed management changes were afoot, however. He said they would be announced before the firm posted its interim results for the year to 31 March during the summer.
The source claimed there would be two or three senior group executive changes. He said if Hyde were to leave the group it would look for an external replacement. The source also claimed group commercial director Rob Johnson was likely to be promoted in a reshuffle.
The Jarvis spokesperson said that some management changes at more junior levels could be expected because of the "amalgamation of the business units of our accommodation services division". He noted: "We would not speculate on those changes before they are finalised."
The troubles at Jarvis led to a sharp drop in the share price to below 130p last week and to speculation that Balfour Beatty was preparing a bid. Balfour denied that this was true. The stock now stands at 150p.
The events last week also led to market doubts over Jarvis' hopes of winning two local authority outsourcing deals – a £250m, 10-year deal to take over Westminster council's highways division, and a £200m outsourcing deal for Salford council's highways and property departments.
A Jarvis spokesperson said: "This approach reflects a common trend within the industry, which sees our competitors involved in consortiums bidding under different names."