  We study genuine entanglement among $3$-qubits undergoing through a noisy
process including dissipation, squeezing and decoherence. We obtain a general
solution and analyze the asymptotic quantum states. It turns out that most of
these asymptotic states can be genuinely entangled depending upon parameters of
channel, memory parameter, and parameters of initial states. We study
Greenberger-Horne-Zeilinger (GHZ) states and W states, mixed with white noise
and determine the conditions for them to be genuinely entangled at infinity. We
find that for these mixtures, it is possible to start with bi-separable state
(with specific mixture of white noise as described below) and end up with
genuine entangled states. However, the memory parameter $\mu$ must be very
high. We find that in contrast to two-qubit case, all three qubit asymptotic
states for $n \to \infty$ are not genuinely entangled.
