Strathclyde Partnership for Transport started using its new ticket system late last year and hopes the new card will replace paper tickets for most passengers.
It is possible for the ticket technology to be used on other modes of transport, like trains and buses, but only if other ticket machines are changed.
John Mason, SNP MSP for Shettleston, asked the Transport Minister Keith Brown if the Scottish Government had had talks with SPT and other transport operators about potential roll out of the smart card.
Mr Mason said he would like the system to be developed into something more like the London Oyster Card. He said: "Having met with SPT recently, I was impressed with the new smart card system that is being developed.
"In moving towards integrated ticketing, however, it is clearly desirable that we link up as much as possible to encourage more people on to using public transport.
"At the moment I am still unclear how joined up the SPT system is with the plans for a national programme.
"Of course, with so many people travelling outside Glasgow and the West for work, it would be good if we could look at something even more joined up with other areas, similar perhaps to what exists in London with the Oyster card."
Yesterday the Evening Times reported on reaction of passengers to this week's price rises of the paper tickets for those not using the smart card, which offers cheaper journeys that single or return tickets purchased at the stations.
Mr Brown said the card was part of a wider programme but also that any extension of its use was a matter for SPT.
He said: "The SPT Subway smart card, or "Bramble Card", is also one of the projects within Transport Scotland's overall Smart and Integrated Ticketing Programme. SPT is represented on the Programme Board which receives periodic updates on progress.
"The details of implementation, and any further use of the Bramble Card beyond Subway, are matters for SPT, subject to any essential inter-operability requirements, for example with the National Entitlement Card."