French driver Pierre Gasly's car caught fire on Friday while there was a crash between Red Bull's Max Verstappen and Lance Stroll's Racing Point car.
The chances of Magnussen and Grosjean remaining in F1 appear bleak, with the experienced pair of Sergio Perez and Nico Hulkenberg also currently without a 2021 seat.
Coronavirus Outbreak: US-owned Haas become fifth Formula 1 team to furlough majority of employees, drivers take pay cuts
The formula1.com website said Haas drivers Kevin Magnussen and Romain Grosjean were also believed to have agreed to a pay cut.
Formula One teams Alfa Romeo and Haas unveiled their cars for the new season on Wednesday.
Formula 1 2019: Red Bull's Max Verstappen takes pole at Brazilian Grand Prix; Lewis Hamilton in third spot
Max Verstappen secured the second pole position of his career to mark his Red Bull boss Christian Horner's 46th birthday in style on Saturday when he topped the qualifying times for Sunday's Brazilian Grand Prix.
Formula 1 2019: Ferrari's Sebastian Vettel tops timing in second practice session of Brazilian Grand Prix
Sebastian Vettel topped the times despite a "scruffy" lap on Friday as Ferrari delivered a resounding one-two to prove they are back on form in second free practice for this weekend's Brazilian Grand Prix.
Formula 1 2019: Haas to stick with Romain Grosjean, Kevin Magnussen in 2020 despite underwhelming performances
Haas were fifth overall last year after two eighth-placed finishes in their opening campaigns in F1 but sit one from bottom with seven races of the 2019 season remaining
Formula 1 Paddock Diaries, Day 1 at Belgium Grand Prix: Reactions to 22 races in 2020, Ricciardo's jokes and Kubica's seat scare
Thursday at Spa Francorchamps was a day of announcements as the dust began to settle with regards to the 2020 grid. Here are some of the most interesting anecdotes and moments from the paddock on Day 1 at Spa.
Formula 1 2019: Haas drivers Romain Grosjean, Kevin Magnussen shrug aside concerns over collisions in recent races
Haas drivers Romain Grosjean and Kevin Magnussen shrugged aside concerns after their recent collisions and said they felt confident of retaining their seats next year.
Formula 1 2019: Lewis Hamilton says he 'totally deserved' three-place grid penalty after controversial incident in Austrian GP qualifying
Stewards handed Hamilton, who had qualified second behind Ferrari’s Charles Leclerc, a three-place drop for impeding Alfa Romeo’s Kimi Raikkonen in qualifying.
Formula 1 2019: Romain Grosjean runs Haas team's upgrade package alone in opening practice at Spanish Grand Prix
Haas has chosen to make a tactical split in introducing its upgrades to try and evaluate their benefit as they bid to overcome a struggle with tyre performance
Bahrain Grand Prix: Ferrari's Charles Leclerc pips teammate Sebastian Vettel to clinch first career pole position
Ferrari new boy Charles Leclerc secured his first pole position when he set a new track record by topping qualifying session for Bahrain Grand Prix.
Abu Dhabi Grand Prix: Lewis Hamilton rounds off successful season with win; retirement-bound Fernando Alonso finishes 11th
Lewis Hamilton's victory at the Abu Dhabi Grand Prix completed a season of total dominance for the Englishman, in which he won his fifth championship.
Russian Grand Prix: Valtteri Bottas pips teammate Lewis Hamilton to clinch pole, Sebastian Vettel to start third
Valtteri Bottas' late fastest lap lifted him ahead of Lewis Hamilton and put a grin back on his face as the Mercedes pair delivered another front row lockout.
Formula One: From Sebastian Vettel surpassing Alain Prost's feat to dream debut for Force India, talking points from Belgian GP
Sebastian Vettel’s tally of career wins in Formula 1 is now 52 - overtaking Alain Prost's record of 51.
German Grand Prix: Sebastian Vettel clinches pole in home race; Lewis Hamilton suffers hydraulics failure in Q1
Sebastian Vettel topped qualifying with a devastating final lap in his Ferrari to pip Valtteri Bottas in the second Mercedes.
French Grand Prix: Reigning champion Lewis Hamilton calls it 'best race' after claiming first win in France
Hamilton now leads Vettel, who had a wayward race, by 14 points in the championship after the first French event for a decade and the first at Le Castellet since 1990.
Spanish Grand Prix: Lewis Hamilton storms to pole with record-breaking time ahead of teammate Valtteri Bottas
Hamilton broke the track lap record with a timing of 1:16.173, 0.040 seconds ahead of his teammate Valtteri Bottas as Mercedes locked up the front row of the grid.
Spanish Grand Prix: Mercedes' Lewis Hamilton tops practice charts; Red Bull's Daniel Ricciardo second fastest
Lewis Hamilton topped the times for resurgent Mercedes in Friday afternoon’s second free practice for this weekend’s Spanish Grand Prix
Spanish Grand Prix Paddock Diaries: From Fernando Alonso's hopes about McLaren’s upgrades to F1’s fan quotient
In his media session, Fernando Alonso estimated that McLaren were up to two seconds slower per lap than the front-running teams.