By Myrmecoleon, I'm going to assume you mean the beast thought in the medieval era to be the result of a mating between a lion and an ant. For those not in the know, it has the face of a lion and the body of an ant, with each part having its appropriate nature.
The short answer is No.
The long answer is that there are too many fundamental differences between the physiology of mammals and insects to allow such a hybrid (the result of natural breeding between animals of different species) or a chimera (the result of genetic manipulation) to occur. There are many reasons for this.
Animals are classified into different categories based on specific characteristics which are unique to each group.
The first and largest difference between mammals and insects is that mammals are vertebrates, meaning they have a backbone and insects are in-vertebrates, meaning they lack a backbone. Further to this, mammal species can be identified by the presence of sweat glands, including those that are specialized to produce milk to nourish their young. Insects are identified by having a chitinous exoskeleton, a three-part body (head, thorax and abdomen), three pairs of jointed legs, compound eyes and one pair of antennae. Insects also lack lungs and 'breathe' through air tubes or pores in the skin. These differences are further compounded by the fact that vertebrate blood contains red blood cells. Insects and other invertebrates, on the other hand, have what is called hemolympha heterogeneous fluid that courses through their bodies. Hemolymph is mostly water, but it also contains ions, carbohydrates, lipids, glycerol, amino acids, hormones, some cells and pigments. The pigments, however, are usually rather bland, and thus insect blood is clear or tinged with yellow or green.
While there are many examples of mammalian hybrids (e.g. mules, ligers, red wolf) and insect hybrids (e.g. Killer bees), these are all done between closely related species. Something like a Myrmecoleon is entirely in the realms of fantasy.