The 30-year-old has travelled with the Championship side on their pre-season tour of Marbella.
The 30-year-old spent three seasons at the Liberty Stadium before being released last summer. And despite the Mail reporting that he had a trial with Leicester City shortly after leaving the Swans, he has been without a club since.
Tiendalli during his loan spell with Middlesbrough
However, the Blues have taken the two-time Netherlands international with them on their pre-season tour of Marbella. And while Rowett insisted that no decision has been made by the player or the club, he did have plenty of praise for what Tiendalli could bring to the table.
"As you can see he's a good player, he's played in the Premier League, has got plenty of pace and he can play left back or right back. He's very versatile," he told the Mail.
"We will see how it goes this week, there's nothing promised either side, it's just we'll have a look at him, he'll have a look at us and see where it goes.
"He says he is in good shape, we will assess that this week."
Tiendalli coming up against Birmingham in an FA Cup tie
With the Blues' first fixture of the new season just over a month away, Rowett will be desperately trying to bolster his ranks to try and help them build on the promise they showed last season.
They are arguably thin in terms of defensive options so the Blues boss will be extremely keen for the former Twente man to impress during his trial as his ability to play on either flank would see Rowett add the kind of depth that he needs without taking a large bite out of the transfer budget.
Birmingham manager Gary Rowett