Schumacher scored his first points in F1 earlier this season.
The son of F1 legend Michael Schumacher has been with Haas for 18 months.
His teammate Kevin Magnussen has already been signed to a multi-year contract.
The contract talks between Mick Schumacher and Haas have suspended for Formula 1’s August break, leaving the future for the 23-year-old uncertain.
German broadcasters RTL and ntv are reporting that Haas has "suspended contract talks" with the 23-year-old:
"Team boss Gunther Steiner is therefore no longer in a hurry to negotiate an extended agreement with the driver," RTL announced, speculating that the latest moves in the 'silly season' have diminished Schumacher's alternatives.
"It means Haas can now rely on the time factor, knowing full well that the team is currently the only way for the German to secure his place in Formula 1."
Given his performance, there is speculation that he could be removed from Ferrari's driver academy with reports saying that Mattia Binotto is "no longer convinced" about the German's potential.
He could then leave the Ferrari program to join another F1 development program - such as Mercedes' or even Red Bull's.
"He has improved compared to last year," Red Bull's top Austrian official Dr. Helmut Marko told Osterreich newspaper.
"But he was always in the Ferrari program, so I never had him on my radar."
All the Aston Martin speculation ended this past week however when Lance Stroll was confirmed for next season to race alongside newly signed Fernando Alonso. That puts young Schumacher perhaps wondering if he will even be on the F1 grind in 2023.