There exists experimental evidence that a dibaryon resonance d' with q
uantum numbers J(P) = O-, T = 0 and mass 2065 MeV could be the origin
of the narrow peak in the (pi(+), pi(-)) double charge exchange cross-
sections on nuclei. We investigate the six-quark system with these qua
ntum-numbers within the constituent quark model, with linear confineme
nt, effective one-gluon exchange at short range and chiral interaction
s between quarks (pi- and sigma-exchange). We classify all possible si
x quark states with JP = O-, T = 0, and with N = 1 and 3 harmonic osci
llator excitations, using different reduction chains. The six-quark Ha
miltonian is diagonalized in the basis including the unique N = 1 stat
e and the 10 most important states from the N = 3 shell. We find, that
with most of the possible sets of parameters, the mass of such a ''di
baryon'' lies above the N(939)+ N(1535) threshold. The only possibili
ty to describe the supposed d'(2065) in the present context is to redu
ce the confinement strength to very small values, however at the expen
se of describing the negative parity resonances N. We also analyze th
e J(P) = 0(-), T = 2, N = 1 six-quark state.