Quantum metrology gives bounds on achievable precision in measurements of parameters like phase delays, frequencies etc. However it is not known if those bounds are saturable and what is the optimal state, i.e. what quantum resources like entanglement should be used to get it. It is known that asymptotically optimal states should be tensor products of some states with lower particle number, thus they would not be highly entangled. Natural class of states which exhibits similar properties are matrix product states and we show that indeed, they are good to solve optimization problems in quantum metrology.