The British team already has a deal with Mercedes that allows them to borrow Stoffel Vandoorne or Nyck de Vries when needed.
Russell, who has been a victim of porpoising over the three days, has acknowledged that the performance from the W13 simply has not been there.
Due to a late red flag caused by Valterri Bottas's stoppage, Max Verstappen only had 20 minutes for a final time attack.
Perez set the fastest time on Pirelli's C4 compound tyres, as Red Bull appeared to shift its focus to performance ahead of next week's race.
Hamilton denied claims that Mercedes were sandbagging at the Sakhir track, despite them finishing behind Ferrari and Red Bull.
Alonso believes Verstappen will now enjoy his time on the track as he prepares to mount his first-ever title defence.
Despite this, the Scuderia and both of its drivers had another productive day, logging a total of 114 laps.
Sainz had led until Magnussen's late 1:33.207s flier, as Ferrari continued to live up to their rivals' claims of being strongest.
Gasly set a time of 1:33.902, replacing Ferrari's Charles Leclerc at the top who went fastest in the first session.
In second place was former Red Bull and current Williams driver Alex Albon, who was half a second behind the Monegasque.