The Glasgow cloud computing business rebuffed approaches from Host Europe Holdings, which is controlled by private equity firm Cinven Partners, of 275p and 285 per share earlier this summer.
The deadline for a firm bid to be made was due to expire tomorrow at 5pm.
But that has now been extended until September 16 as Iomart revealed Cinven has made a proposal of 300p per share in cash.
Cinven said last night that Iomart chief executive Angus MacSween, finance director Richard Logan and operations director Sarah Haran, who together had a total stake of 18.5 per cent in the Glasgow company, had indicated their support for its proposal. It added that the independent directors of Iomart had given their consent to these three executives working with Host to finalise its proposal.
Iomart said: "The Panel on Takeovers & Mergers has consented to an extension of the relevant deadline to enable Cinven to conduct initial due diligence and enable the parties to conclude their ongoing discussions."
However Iomart, which employs around 200 of its 375 staff in Glasgow, admitted there was no certainty an offer would be made.
If the 300p offer is tabled and accepted it would leave Mr MacSween in line to receive a windfall of more than £50 million.
His 16.8 million shares are equivalent to around 15.75 per cent of the business.
Bill Dobbie, the former Cupid chief executive who is Mr MacSween's brother-in-law and helped set up Iomart in 1998, would see his 3.45 million shares valued at in excess of £10 million.
Institutional investors such as Liontrust Asset Management, Majedie Asset Management, Old Mutual Global Investors (UK) and Henderson Global Investors are among other large shareholders.
Shares in Iomart, which listed on the Alternative Investment Market (AIM) in April 2000 and has pursued a buy-and-build strategy, ended the day up 12.5p at 279.75p.
The company has around 350,000 customers, owns six data centres and has a 1,860 kilometre fibre optic network.
Cinven entered the European IT market when it bought London-based Host Europe in August with the deal valued at around £438 million.