The Eagles boss was disappointed with the club's business - or lack of it - in January saying Crystal Palace "did not do particularly well" in terms of strengthening the squad with only three arrivals.
Hodgson has told his Crystal Palace bosses that he wants more this summer, saying: "I am hoping this summer we won't be able to use as an excuse that we didn't have the time, and I hope that we won't be able to use as an excuse that we didn't identify the players.
"Of course I don't write cheques and make those decisions, all I can do is recommend and hope that the club can help us to bring in the players that we think are the right ones to make us even stronger next year."
Aside from Bordeaux, who want to make his recent six-month loan spell permanent, Crystal Palace are said to be among the favourites for his signature.
Hodgson faces competition from German side Werder Bremen for a player who has represented France at youth level from Under 16s all the way up to Under 20s.
The 24-year-old is under contract with Monaco until 2022 and is rated highly by managaer Leonardo Jardim who L’Équipe claim still hopes Meite can become a first team star.
A sizeable bid from Crystal Palace could sway Monaco's thinking, though, as they are historically a selling club at the right price.