Mean square matrix elements of the time reversal invariance violating (TRIV) interaction between the compound nuclear states are calculated within the statistical model, using the explicit form of the TRIV interaction via the ρmeson exchange. From the comparison of the calculated values with the data known for p + 27 Al ⇔ 24 M g + α reaction, and for γ-correlation measurements in 113 Cd(n, γ) 114 Cd process, the bounds on the TRIV constant are obtained g ρ < ∼ 1.8 × 10 −2 andḡ ρ < ∼ 1.1 × 10 −2 . The sensitivity of the recently proposed detailed balance test experiments on isolated resonances in 32 S to the value ofḡ ρ is shown to be as high as to reach valuesḡ ρ ∼ 10 −4 .