Finch himself sounded as if he wouldn't be averse to going in the other direction and playing in the Pakistan Super League
Aaron Finch must have had the hearts of Melbourne Renegades fans all a flutter when he appeared to signal a fantastic signing coup for his BBL team.
"I just asked Babar (Azam) if he's interested in coming and playing for the Melbourne Renegades and he certainly is - and, hopefully, we can announce that signing tomorrow!" declared Finch in Lahore on Saturday.
Following deep breaths all round, the Australian captain and long-time Renegade then grinned: "Only joking..."
It may have been just a bit of mischief but Finch was deadly earnest in expressing his hope that Babar and some of the other outstanding talents in the ODI side which had just hammered his team might grace the Australian T20 scene next summer.
"It would be great to have more world-class players in our domestic competition," said Finch.
"Babar is obviously as good as anyone for a long time in this format of the game and T20 cricket," he added, after suffering the Pakistan captain's second successive matchwinning century - a series-clinching 105 not out - in the space of three days.
"We also talked about Shaheen's strength ... he's a fantastic bowler," added Finch, referring to Pakistan's devastating left-arm paceman.
"The talent of Pakistan cricket is extraordinary. I think world cricket is better when Pakistan are playing well and world cricket is better when they have the opportunity to play in our domestic league."
Haris Rauf, who trapped Finch lbw for a duck on Saturday, has already become a Big Bash fan favourite with the Melbourne Stars but Babar, the world's top-ranked batter in both ODIs and T20Is, would be the real big catch.
"If Babar Azam is available to play Big Bash, any team would love to have him," enthused Finch, after his captain counterpart sealed the player of the series award.
"Any of the Pakistan guys, we love having them as part of our competition.
"Any opportunity that they can fit into out comp is fantastic and they'll always be welcome in the Big Bash."
Finch himself sounded as if he wouldn't be averse to going in the other direction and playing in the Pakistan Super League T20 competition.
"It all comes down to waiting until the schedules are released and seeing where there's gaps in the schedule. I've loved my time here in Pakistan and I've loved the tour," said the 35-year-old.