Reports had suggested the ICC was considering the Welsh capital, along with Colombo and Singapore, to replace Dubai as the sight of the world governing body's administrative base.
The proposal was said to have been made in a leaked working paper of the ICC's financial and commercial affairs committee.
The ICC was based at Lord's until 2005 before moving to Dubai, and Glamorgan have confirmed initial talks have taken place about the organisation coming to Wales.
A Glamorgan statement read: "Discussions are at a very early stage and ongoing, with Cardiff being only one of a number of possibilities being considered."
A Welsh Government spokesperson said: "We have engaged in discussions on the matter but at this stage any details would remain commercial in confidence."
Cardiff was one of three host cities for the 2013 Champions Trophy, as well as one fixture in the 1999 World Cup.
The SWALEC Stadium also staged the first Test of the 2009 Ashes series.
The ICC 'position paper' also included a plan that would see the England and Wales Cricket Board (ECB), in conjunction with Cricket Australia (CA) and the Board of Control for Cricket in India (BCCI), become the three central figures for major decision-making both on and off the field.