Reja replaced Vladimir Petkovic halfway through the campaign but his failure to deliver UEFA Europa League football has him facing the sack, despite signing a contract until June 2015.
That uncertainty has led to rumours of Banfield coach Almeyda returning to the Stadio Olimpico after a highly successful three-year spell in Rome between 1997 and 2000, where the former Argentina international midfielder won the Serie A, UEFA Cup Winners' Cup, UEFA Super Cup, Coppa Italia and Supercoppa Italia.
And the 40-year-old, who guided River Plate back to Argentina's top flight in 2012 before joining Banfield, has openly expressed his desire to take charge of Lazio next season.
"It would be a dream to go back to Lazio," Almeyda told ilcatenaccio.es.
"I truly respect the work done by Edy Reja and don't want to create any pressure on him, but at the same time I can’t disguise it would be wonderful to return to Lazio as a coach.
"It's a shame to see Lazio reduced to this and I will always have this club in my heart. I always liked the Rome derbies, especially as I usually had to mark Francesco Totti, who was the spoilt child of Roma.
"He is a fantastic player and I was always motivated to face him, because he's a player with so much quality."
