The Blues were not expecting to do any major business in January but are prepared to sell Salah, who is yet to start in the Barclays Premier League this season.
Roma had hoped to take Salah on loan but Chelsea have told the Italian giants they would have to make the switch permanent at the end of the campaign.
Press Association Sport understands Chelsea are demanding 1m euros (Â£760,000) for an initial six-month loan spell, with an obligation to pay another 14m euros (Â£10.6m) in the summer.
The deal would see the Blues recuperate the fee they paid Basel to sign Salah just 12 months ago
It is understood, however, Roma view that package as too expensive for a player who has managed only two goals in almost 14 months.
Roma are also in negotiations with Dnipro for Yevhen Konoplyanka and will turn their attention to the Ukraine playmaker if Chelsea refuse to soften their stance.
Andre Schurrle has also been linked with a move away from Stamford Bridge, with both Borussia Dortmund and Wolfsburg reportedly keen.
Wolfsburg sporting director Klaus Allofs, however, insists they hold no interest in signing Schurrle and told Press Association Sport: "There is nothing in it whatsoever."
Jose Mourinho would be happy to end the January transfer window with his current squad, despite being linked with a big-money move for Fiorentina's Colombia winger Juan Cuadrado.
Chelsea have made contact with the Italian club about Cuadrado's availability but it is believed a formal offer will only materialise if Salah or Schurrle are sold.
Fiorentina, who are sixth in Serie A and chasing Champions League qualification, do not want Cuadrado to leave mid-season but would be helpless should Chelsea trigger the player's Â£26.8m release clause.
Source : PA