He believes that Seaq, the existing system, could be modernised in stages and paid for out of the exchange's resources. He said market estimates of a pounds 75m bill for updating Seaq were 'excessive'.
But some senior City figures, wounded by the pounds 300m to pounds 400m costs of Taurus, are opposed to the exchange starting another project for fear that it too could collapse, leaving them to pay the costs.
Taurus, which would have replaced share certificates with electronic records, was abandoned last month after the exchange admitted that the project, already much delayed, was running late and over budget.
The chief executive, Peter Rawlins, resigned, and a search has started for a replacement, who is unlikely to be appointed before the autumn.
Mr Hugh Smith has launched a series of meetings with heads of stockbroking firms in an attempt to recover the City's backing. 'We have to rebuild confidence. A lot of work and effort is required,' he said yesterday.
Speaking ahead of Thursday's board meeting, which is taking place against a background of a wide-ranging debate about the exchange's functions in the wake of the Taurus fiasco, Mr Hugh Smith said: 'The exchange is there to transform savings into long-term capital for industry.
'In terms of the primary market (new issues) this means it is the competent authority for listing and it organises the flow of company news. It organises and regulates the secondary market (trading).'
The board is expected to agree that Topic, the exchange's screen-based news service, should be farmed out to a software firm. But the exchange will keep responsibility for collecting information on share deals and checking companies' announcements.
These are relayed to news agencies such as Reuters through the regulatory news service, which would be unaffected by contracting out Topic.
The exchange is also prepared to lose responsibility for settlement - processing share deals - once a successor to Taurus is chosen. But the exchange wants to retain its other roles, notably its remaining regulatory functions.
The outcome depends on a review of the role of the Securities and Investments Board by Andrew Large, its chairman. There is speculation he will recommend that some of the exchange's regulatory functions, including investigation of insider dealing, could be transferred to the SIB.
It is understood that Mr Hugh Smith believes the updating of Seaq could be a first step to dividing the market into two, serving professionals and individuals respectively.
But he is anxious to avoid upsetting market-makers who fear that segmentation will result in the expansion of order-driven systems that by-pass the market-making system used for large stocks.
One Stock Exchange insider said: 'We have to persuade them there is no hidden agenda. We still believe market-makers should be at the heart of the system. They do not however make liquid markets in some of the smaller stocks.'Reuse content