Not a good idea. In a nutshell, transcendental meditation is an eastern (Hindu) meditation technique that involves repeating a mantra (usually a Sanskrit sound) designed to bring the practitioner into a “higher form of consciousness” for the purpose of finding God within himself. This technique conflicts with authentic Christian prayer, whose goal is not to seek God in self but to flee self to the “You” of God.
In the Letter to the Bishops on Some Aspects of Christian Meditation (Congregation of the Doctrine of the Faith), Christian prayer is explained in this way:
3. Thus Christian prayer is at the same time always authentically personal and communitarian. It flees from impersonal techniques or from concentrating on oneself, which can create a kind of rut, imprisoning the person praying in a spiritual privatism which is incapable of a free openness to the transcendental God. Within the Church, in the legitimate search for new methods of meditation it must always be borne in mind that the essential element of authentic Christian prayer is the meeting of two freedoms, the infinite freedom of God with the finite freedom of man.
12. With the present diffusion of eastern methods of meditation in the Christian world and in ecclesial communities, we find ourselves faced with a pointed renewal of an attempt, which is not free with dangers and errors, “to fuse Christian meditation with that which is non-Christian.”