Are you catching is weird. Catch is unlikely to be an action in progress as it only takes a second. The other two have almost opposite meanings. Holding means the suspect has been caught already. Getting means the police are in the process of acquiring the suspect. This is also weird. The police do not get suspects. What about looking for, searching for, hunting, tracking down? If the suspect has already been caught, holding is good.

It's hard for me to know exactly what you're referring to. Are you referring to intention to watch/observe, or track down / find, or hold temporarily in the street (detain), or hold longer and bring to the station (arrest), etc. I need to know which stage of the pursuit has already begun, and which stage is being questioned (and is it a question of entering into that questionable stage, or prolonging that questionable stage). If you can supply these details, then I can provide an appropriate sentence. Otherwise, it would be wild guesswork and probably not what you need.