Nowadays, even with the existence of many Cloud Providers (CP) in the market, it is still impossible to see CPs who guarantee, or at least offer, an SLA specification to Cloud Users (CU) interests: not just offering percentage of availability, but also guaranteeing specific performance parameters for a certain Cloud application. Due to (1) the huge size of CPs’ IT infrastructures and (2) the high complexity with multiple inter-dependencies of resources (physical or virtual), the estimation of specific SLA parameters to compose Service Level Objectives (SLOs) with trustful Key Performance Indicators (KPIs) tends to be inaccurate. This paper proposes the initial design and preliminary approach for an SLA Support System for CC (SLACC) in order to estimate in a formalized methodology - based on available CC infrastructure parameters - what CPs will be able to offer/accept as SLOs or KPIs and, as a consequence, which increasing levels of SLA specificity for their customers can be reached.