Sky Sports revealed on Tuesday that former Aston Villa and Sunderland defender Cuellar had joined the training ranks at Ewood Park.
Ex-West Ham defender Spence and experienced goalkeeper Ashdown are also hoping to catch the eye, with Bowyer prepared to give them every opportunity to earn a permanent deal.
He said in the Lancashire Telegraph: “Jordan’s trained with us on Monday and Tuesday, so we’re having a look at him.
“We’re not blessed with too many defenders so he’s spending a couple of days with us and playing in a game this week and we’ll take it from there.
“Carlos is another one who trained with us on Monday. He asked if he could come and train with us and that’s what he’s done.
“He’ll look to probably continue that. He’s using us in terms of getting fit and training and it presents us with the chance to have a look at him as well.”
Bowyer is aware of the need to bolster his ranks ahead of the new Sky Bet Championship season, with slow progress made in the transfer market so far.
He added: “We could do with adding one or two in terms of the strength in depth, but I’m no different to everybody else who is saying that.
“We’ve only brought two in permanently so we’ve not been really active this summer, but throughout the course of the season we might need to improve the numbers.
“That character is really important to us. We don’t just bring anybody in. We check on the character first and foremost and then it’s up to the player to show us what he is capable of.
“Every situation is different. For some players they just want to come and join in training because they’ve something else lined up, and I’m fine with that if we know them and we know what they’re like.
“Then there are other situations where players are trying to fight for a contract.”