Claude-Maurice scored 17 goals in 55 appearances for the Ligue 2 side and Arsenal were keen to make a move.
Indeed, the Gunners are believed to have made a bid for the 21-year-old last week.
West Ham are also linked with the winger, but the France Under-20 international does not see his future in England.
“Now I feel like it’s time to leave, to join a club that is playing at a higher level,” Claude-Maurice told L’Equipe.
“I want to join Monchengladbach. It is a club that relies on young people, there is a good structure, the team will play in the Europa League.
“This project pleases me and suits me.”
Reports suggest that Lorient want around £18million for Claude-Maurice.
Arsenal boss Unai Emery is keen to improve his squad this summer though is on a tight financial budget.
But former Gunners striker believes Arsenal should do all they can to bring in the rising Lorient star.
“For the money that we talk about I think he’ll make it,” he said.
“It’s about taking a gamble now when other teams aren’t prepared to.
“The market has gone so crazy in the last few years. If you want a top level international it’s nothing cheaper than £40m.
“He’s a good player and has really good qualities.
“I remember incredible quick feet, a technical player. Technically he was amazing.
“The only thing – he was young at the time – was making the right decision, passing when you need to pass.”
Arsenal are yet to make a signing this summer after a fifth-placed Premier League finish.
The Gunners also reached the final of the Europa League, but were beaten by Chelsea in Baku.