Addicks boss Alan Curbishley has been tracking the 22-year-old for some time and has now taken a closer look at him.
Cambridge gave Charlton permission to let Guttridge train with them and his representative Richard Cody confirmed he had spent time at The Valley.
"It went very well," he told skysports.com.
"Alan has been looking at Luke for a quite a while, and he, along with Mervyn [King] and Keith [Peacock] wanted to see him in training.
"Because of our good relationship with Cambridge, we were able to get Luke to Charlton, despite him being under contract."
Guttridge only signed a new two-year contract with Cambridge earlier this year, but The U's always knew their prized asset would attract attention.
Charlton are now in pole position to seal his signature.
"They now have first refusal on him," added Cody. "It is only right, any club coming in for him will be made aware of the situation.
"We do not expect any sort of decision until much later in the summer."
