Palmieri, 27, was sent out to the French club last summer but the Blues now want him back at Stamford Bridge this month to replace sidelined Ben Chilwell.
According to Guardian reporter Fabrizio Romano, Chelsea's request has not gone down well at the Parc Olympique Lyonnais though, with Les Gones turning down two approaches.
Romano confirmed Chelsea are now taking their attempts to recall Palmieri up a notch, offering the French top flight club €4million (£3.3m) in compensation for bringing the left-back home early.
But if this third push fails then Chelsea still have a 'plan B' in their hands.
Palmieri has cemented himself in the Lyon first-team, making 17 appearances in Ligue 1, scoring one goal and recording one assist, and he played in their 1-1 draw with league leaders Paris Saint Germain last weekend.
The Brazlian-born Italy international joined Chelsea from Roma in 2018 on a four-and-a-half year deal for €20m (£16.7m) plus add-ons, but had been unable to secure a starting spot in west London.
Now, Tuchel's side have seen their options depleted with Chilwell out for the season after tearing his anterior cruciate ligament (ACL) in November - leaving room for Palmieri to challenge Marcos Alonso.
The European champions have also been linked with left-back Lucas Digne as a possible replacement, however Romano has since stated a deal with the Everton defender is now most likely off the cards, while they could also recall Ian Maatsen who is currently on loan at Coventry.