The 28-year old Englishman is available as a free agent after ending a four-year stint with lower league club Oxford United at the end of last season.
Batt, who can be deployed as a full-back on both sides, posted a picture of BC Place on Twitter on the weekend suggesting that perhaps he was set to sign a contract with the Whitecaps.
Additionally, he told reporters: "I've heard some great things from Nigel [Reo-Coker] and a few of the other players. I've spoken to them for the last four weeks about here, so we'll see what happens.
"I'm more comfortable at right back, but I'm both-footed. But I'm just happy to play football. I love the game that much."
However, Vancouver head coach Martin Rennie said nothing had yet been finalised.
"Damian's here on trial," Rennie said. "He's here for the week and we'll get a good chance to look at him. We like what we've seen and we're just interested to see a little bit more, so it's nice to have him here."