Marshall was a guest of the NZRU at the Bledisloe Cup game against Australia, after which Tew admitted an informal approach had been made.
But Tigers CEO Stephen Noyce launched an immediate response, and Marshall's agents remained cautious.
Noyce said: "He is obviously an important player to our club. He is in his first full year of NRL and will be the first to admit he still has a lot of learning to do.
"We hope he will be part of our club for a long time to come."
Brett Papworth, director of Marshall's management agency Tauber Group, added: "The NZRU spoke to us mid-last week making inquiries whether there was a point in showing any interest in Marshall.
"We told them he was pretty happy where he is and a move back to New Zealand or a switch to union was not on the radar.
"Knowing he is a big fan of Kiwi sport, they asked us if he would like to go to the All Blacks game, which we knew he would."
At the game Marshall sat with family and friends of the All Blacks and did not talk with management, Papworth said.
"Like all Kiwis I am sure he wanted to grow up to be an All Black, but if that is on the cards it would be a long way down the track.
"The All Blacks team is pretty strong at the moment, so any move would be a big, big risk."