Chelsea field Frank Lampard and Nuno Espirito Santo as possible substitutes for Maurizio Sarri.
The Italian is almost certain to be eliminated at the end of the season, unless Chelsea's sad season falls further, in which case the ax may fall earlier.
Nominated in the summer 2018, the leaders of Chelsea now believe that the Italian is not a good candidate for the club, after a season in which the initial credentials of the title have crumbled and the players have appeared unhappy with the methods of the manager.
The besieged Blues still have a realistic chance of qualifying for the next Champions League season, finishing in the top four of the Premier League or winning the Europa League. They will face Slavia Prague in the quarter-finals of next month.
If the Czech team beat them, and the difficulties of the team lead them to a three-way match with Arsenal and Manchester United, the owner Roman Abramovich will act to remove Sarri before the end of the season, with the former chief Stamford Bride favorite of Lampard and Lupi Espirito Santo the names found at the top of the Russian wish list.
The wolves enjoyed a sensational return to the top flight under Portugal, sitting seventh in the league and having booked a first FA Cup semi-final in 21 years, and exposed Chelsea's shortfalls under Sarri with an excellent away performance to request a 1- 1 draw at Stamford Bridge earlier this month. Only one goal at Eden Hazard last minute denied visitors a deserved victory.
The club's top scorer Lampard is currently in charge of Derby County, where he led the team to eighth place in the championship, a point off the playoffs with one game less.
Abramovich had hoped to appoint Zinedine Zidane or Max Allegri as manager for next season.
The Juventus boss, Allegri, moved away from work, while Zidane made a surprise comeback at the former Real Madrid club after Santiago Solari was fired.