Chelsea goalkeeper Thibaut Courtois has kicked off his rehabilitation after undergoing surgery to correct a serious knee injury.
The Telegraph state that Mourinho has so far been pleased with the form of Begovic, who joined the club over the summer from Stoke City, and will keep the Bosnian global as his first choice until Courtois returns.
Mourinho is anxious that he could be left short if Begovic suffers an injury, which has prompted him to look at free agent Amelia.
Amelia has represented his country in the past and played for the prestigious Milan club.
Chelsea have also been linked with Helton Arruda, the Porto goalkeeper, but Mourinho is concerned that he would only be available in January.
Mourinho previously admitted his desire to bring in a new goalkeeper, but ruled out a move for Porto custodian Helton.
The champions named only 19 players over 21 in their 25-man Premier League squad at the start of the month, including five who are considered “homegrown”, meaning they can apply to register a free agent outside the transfer window.
Having left Milan in 2014, Amelia spent time with amateur outfit Rocca Priora, before joining Perugia in January. “By then, Courtois will be available again”.