The Leicester manager previously worked with the Manchester United director of football during his time in charge at Southampton, but says that history won't stop him defending Page, an 18-year-old midfielder increasingly regarded as one of the brightest talents outside the Premier League.
"Louis is a really fantastic young player. Obviously, I know the director of football at Manchester United very well after spending some time with Southampton. So we haven't actually spoken with Louis because he probably knows what I'd say to him and tell him to go away," Martin told Sky Sports, only half-joking.
"But no, until something comes in that is really brilliant for the club, the player, and everyone is happy, then Louis stays, and he's in the squad.
"I'm really enjoying working with him. He's a fantastic young player."
Page, who was named EFL Apprentice of the Year last season, has already made 21 senior appearances for Leicester, including five Championship starts during their relegation campaign, and played in Saturday's Carabao Cup win over Northampton as the club begins life in League One under Martin.
He joined the Foxes' academy at Under-9 level and signed his first professional contract in September last year, a deal that means United would need to agree a transfer fee rather than simply wait for his contract to expire.
"After joining us at Under-9s, Louis has progressed through our Academy ranks and developed within the LCFC pathway into one of the brightest talents in our system," the club said when he turned professional.
Leicester have already lost one of their most highly rated academy graduates this summer, with 17-year-old forward Jeremy Monga completing a move to Manchester City. Losing Page too, so soon after relegation, would be a further blow to a rebuilding project Martin is trying to establish at the King Power Stadium, and Arsenal and Aston Villa have also been credited with an interest in the England Under-20 international alongside United.
Reports suggest Page would be open to a move to Old Trafford if the opportunity arose, but with Leicester determined to keep hold of him unless an exceptional offer materialises, any deal is likely to take time to resolve. For now, Martin's message is clear: Page remains firmly part of his plans as Leicester look to bounce straight back from relegation.