I was reading about quantum teleportation using Qiskit. Alice wants to teleport some quantum state to Bob. My question is Is it possible for bob just to see the state vector after receiving it from Alice without measuring it?
No, this is not possible. The state vector describes a distribution of a possible outcomes after measurement the quantum state. So, to reconstruct the state vector, the measurement has to be performed.
If you can assume that the amplitudes in the state vector are real numbers only, you can only repeat the measurement several times in the computational basis to get reasonable statistics.
However, when a quantum phase is involved (i.e. the amplitudes are complex), you have to measure in other bases (e.g. Hadamard)as well or do complete tomography to reconstruct the state vector.
Note that in Qiskit you can employ
statevector_simulator which reveals the state vector, however, as the name suggest, it only a simulation on a classical computer. In quatum world, the measurement (even repeated one) is necessary to get the state vector.