"The ultimatum is sure to anger Sydney Sixers officials in South Africa trying to win the lucrative Twenty20 tournament with Watson's help."
The newspaper said the CA is concerned about a possible injury breakdown hampering the all-rounder, who was named World T20's Player of the Tournament.
"Officials are worried Watson could burn out after a starring performance in the World Twenty20, and now the demands with both bat and ball for the Sixers in the Champions League."
If Watson is asked to come back, he would play just two games -- against Yorkshire on Tuesday and Highveld on Thursday.
"It means he will miss next Monday's final game against Sachin Tendulkar's Mumbai, which could decide if the Big Bash League champions progress to the finals and close in on the $2.5 million winners' pay cheque."