The former English County champions have been seriously weakened in their bowling ranks and sought help ahead of their opening match of the Limited Overs tournament on Friday.
Pakistani spinner Saqlain Mushtaq will miss the rest of the summer with a serious knee injury and pace bowler Azhar Mahmood is unlikely to feature in the group stages with a troublesome back.
A nagging groin injury also means former England seamer Martin Bicknell will miss a minimum of two weeks whilst Jimmy Ormond will miss the first two games of the Twenty20 Cup due to problems in both knees.
Blewett, who has played 43 Tests for Australia, has previously had successful spells as an overseas player for Yorkshire, Nottinghamshire and Kent.
Surrey told the BBC they originally wanted a spinner but have now widened their search to include Blewett who is listed as a batsman but can step in and act as an additional slow bowler.
"We are looking for someone to play in place of either of the injured Pakistanis," said a spokesman for the Lions.
"We've looked around for a spinner but there aren't many around especially as the Asia Cup is about to start."