Suaalii refused to stoke the personal duel that has emerged between him and Scotland centre Sione Tuipulotu.
He hit Tuipulotu with a big tackle in the first half of the Wallabies' defeat at Murrayfield in the autumn, sparking an exchange of words.
Suaalii, who suffered a wrist injury in their collision, was heard to say, apparently to Tuipulotu, that he would "see you next time" as he left the field.
"Not really to be honest," he said, when asked if such personal battles fuel him.
"I am really just focused on what I can bring best for the team, but anyone in the Lions I am ready to go against them."
After initially crossing codes, Suaalii played at outside centre, but his most recent outings for the Waratahs have been at full-back, where he was named in the Super Rugby Pacific team of 2025.
"It makes you a better rugby player, seeing the game from a different perspective always helps you," he added.
"I am very confident in playing wing, centre and full-back."
Suaalii is targeting a return to action in the Wallabies warm-up Test against Fiji on 6 July. The Tests against the Lions take place on 19 and 26 July and 2 August, kicking off at 11:00 BST.
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