A spokesman for Mr Sugar confirmed that he held a preliminary meeting yesterday with the administrators, PricewaterhouseCoopers, and with representatives of Ionica.
The spokesman added: "No further statement will be made unless a more meaningful outcome were to evolve."
Observers suggested that an outright takeover of Ionica by Mr Sugar looked unlikely, and there was puzzlement over what his exact interest in the telephone business might be.
Ionica pioneered a radio-based technology for sending telephone calls through a small aerial attached to the side of a house.
Amstrad's past ventures include manufacturing the equipment to receive satellite television.
But Ionica needs a substantial injection of funds, estimated to be at least pounds 300m, to continue rolling out its network of base stations. This would require a large financial commitment from any would-be rescuer.
Mr Sugar is among between 10 and 20 parties who have expressed an interest in Ionica to the company's administrators. The administrators were called in after Atlantic Telecom pulled out of negotiations to rescue Ionica.
Earlier this week the administrators made 600 of Ionica's 1,000-strong workforce redundant. They have kept on sufficient staff to ensure that customer services are not affected and the business can continue to be run.
As of last Monday, only 62 out of Ionica's 62,000 customers had left the company, and some had even offered to pay their bills early to help the company stay in business.
Ionica shares were floated at 390p in July 1997, valuing the company at pounds 659m. They were suspended at 17.5p last week, leaving it worth less than pounds 30m.