The former forward thinks it would be curtains for the Frenchman if his compatriot made the move.
The Gunners have been linked with a move for the French star all summer, with many saying that they need a striker of his calibre to complete their squad and be able to challenge for the Premier League title.
So far, a move has failed to materialise, with Rafa Benitez’s side looking unlikely to sell this late into the summer transfer window. Should a move happen though, Nicholas believes that would be the end of Giroud at the Emirates.
"I do think he'll actively be searching the market and if nothing comes up he won't buy for the sake of buying,” he told Sky Sports.
"If Benzema was to become available for say £40m and he felt he was going to make the side better he'd sign him and you sell Giroud or one or two other players.”
Wenger only interested in improvements
The former forward also believes that Wenger will only sign more players this summer if he knows he can vastly improve his squad in the process.
He has only added Petr Cech to his team so far this summer, with his addition representing a vast improvement on what he already has available to him in the shape of David Ospina and Wojciech Szczesny.
Signing Cech has been considered a major coup for the French boss by many, and Nicholas says his signing, as well as the ones of Mesut Ozil and Alexis Sanchez in the past show the long serving manager has become more adaptable in the market.
"He'll only go into the market if he knows he can get better players than he's already got,” he added.
"Over the last few years he's spent a fortune on Ozil and Sanchez. He brought in the experience of Mertesacker and now he's brought in Cech so he's been more adaptable than he maybe was in the past.”