Gary Rowett is running the rule over defender Tiendalli, 30.
A versatile performer who can play in both full-back positions, Tiendalli is a free agent.
He flew out with Blues to Spain from Birmingham Airport on Monday morning and will be part of the First Team Squad during the camp at the Marbella Football Centre.
Surinamese-born Tiendalli in the FC Twente team that won the 2009-10 Eredivisie.
He moved to Swansea City in 2012 and in his first season earned a League Cup winners' medal and was called-up by Holland.
At the end of his third season with the Swans he was loaned to Middlesbrough.
Tiendalli has two full caps and 16 Under-21 appearances to his name.
"Dwight's one we were aware of last year," said Rowett. "He is obviously a free agent, he was due to come in next week but we asked him if he would like to come out with us on tour. He has fitted in really well with the players so far.
"It's never easy when you turn up at the airport and travel away and train with a new group of players.
"But 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.
"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."
In the last campaign Tiendalli was hampered by injury as he sought a club.
"He played games early in the (previous) season but he had a bit of knee injury towards the middle of the season. Ironically I think Ewan Chester said they wanted to take him on loan at Brighton such was his quality.
"Then he has had a season where towards the end he has not been fit, when you get to that point and you are out of contract you make sure you are fit and ready to go.
"That's where he is. He says he is in good shape, we will assess that this week."