According to Izvestia, the former Manchester City forward has fallen out of favour under new manager Leonid Kuchuk and is ready to quit Russia either permanently or on loan.
None of his other frontmen, Mladen Petric, Carlton Cole or Modibo Maiga have yet to find the net in the Premier League, and therefore Allardyce is hoping to recruit further reinforcements when the transfer window reopens.
He is reportedly a fan of Caicedo, and the Colombian's agent, Jose Chamorro, has admitted that his 25-year-old client could be available as he is interested in a fresh challenge.
He told reporters: "Caicedo's game has long earned the attention of many European clubs.
"Naming any specific team does not make sense, but I don't mind saying that there are clubs from Europe's leading championships interested.
"However, I should note that Felipe respects his current contract with Lokomotiv and he will leave only in the event that the club are satisfied with the proposed terms."
Caicedo has scored five goals in 35 league games since making a £6m switch to Lokomotiv in 2011.