How do you describe these animals' action/ state before attacking their prey?

Solution 1:

The usual verb is stalk which is defined by Merriam-Webster as:

to follow (an animal or person that you are hunting or trying to capture) by moving slowly and quietly.

Solution 2:

Consider poised to pounce or poised to strike.

Poised:

balanced and prepared for action

(Collins)

From Bicycling Magazine's Mountain Biking Skills, p69:

When felines are poised to pounce, they're loose, not rigid.

From Gavin Ehringer's Western Horseman's Rodeo Legends:

Like a lion poised to pounce, Whitfield sets up for a winning run at La Fiesta de los Vaqueros Rodeo in Tucson.

I think that felines pounce and snakes strike, but that's not absolute.

Solution 3:

I would say the feline is crouching, ready to pounce. See the images of ready to pounce google gives you (I reproduce some here):

Crouch in Oxford Learner's Dictionaries:

1 to put your body close to the ground by bending your legs under you

Pounce in Oxford Learner's Dictionaries:

to move forward suddenly in order to attack or catch someone or something
The lion crouched, ready to pounce.

Solution 4:

While stalking their prey, predators get as far down on their haunches as possible as soon as they're ready to pounce. This allows them to store energy in their tendons, that enables them to close what distance is left in a heartbeat.

Of interest may be the classic swishing of the tail, which is thought to betray their anxiety about whether or not, and at which moment, to strike.

Solution 5:

I would suggest "lie in wait," meaning to conceal oneself, waiting to surprise, attack, or catch someone. [OxfordDictionaries.com]

Some of the images included in the question show animals stalking their prey, but the verbal description of the phrase sought by the original poster leads me to believe that that is unintentional.