The poor pooch who allegedly got roughed up by Twitch streamer and rapper Aspen Kartier won't have a problem finding a new home ... if the dog is ever put up for adoption.

Since Aspen's arrest for allegedly beating a 3-month-old Maltipoo, the pup has been in a foster home ... and we've learned hundreds of folks are making calls to see if they can adopt the dog.

LifeLine Animal Project in Georgia tells us Aspen's dog is safe, recovering well and receiving the care and stability he needs in a temporary foster home.

Despite hundreds of families offering to adopt the dog, LifeLine tells us Aspen's dog is NOT currently available for adoption because her case is still active and pending.

As we reported ... Aspen was busted and charged with animal cruelty after a video of her seemingly roughing up an innocent pup on stream went viral. Aspen is now banned from Twitch until late March and she's denied the allegations, saying her dog is just fine.

We're told DeKalb County Animal Services is telling those who call to express interest in adopting the dog that there is no estimated time frame for when he may become available for adoption.

If the dog is every put up for adoption, he will be listed on the county's adoption website on a first-come, first-serve basis.

In the meantime, we're told there are more than 450 animals in the DeKalb and Fulton County animal shelter that need loving homes as well.

LifeLine Animal Project says anyone interested in giving a deserving animal a second chance can view adoptable pets at lifelineanimal.org/adopt.