Let R be a ring and n a fixed non-negative integer. $cal{TI}_n$ (resp. $cal{TF}_n$) denotes the class of all right R-modules of FGT-injective dimensions at most n (resp. all left R-modules of FGT-flat dimensions at most n). We prove that, if R is a right $prod$-coherent ring, then every right R-module has a $cal{TI}_n$-cover and every left R-module has a $cal{TF}_n$-preenvelope. A right R-module M is called n-TI-injective in case $Ext^1$(N,M) = 0 for any $N;{in};cal{TI}_n$. A left R-module F is said to be n-TI-flat if $Tor_1$(N, F) = 0 for any $N;{in};cal{TI}_n$. Some properties of n-TI-injective and n-TI-flat modules and their relations with $cal{TI}_n$-(pre)covers and $cal{TF}_n$-preenvelopes are also studied.