Managerless Tottenham will come up against Ramos after being drawn to face Ukrainian outfit Dnipro in the last 32, while Swansea have been tasked with overcoming Serie A title hopefuls Napoli.
Ramos was in charge of Spurs for just under a year from October 27, 2007 before being sacked with the club bottom of the Premier League in the 2008-09 season having taken just two points from their opening eight matches.
He will therefore be intent on gaining a measure of revenge over his former side, who announced the sacking of Andre Villas-Boas on Monday morning despite the Portuguese overseeing a 100 per cent record in Europe this season.
Tottenham topped Group K with six wins from as many matches and will be regarded as one of the favourites to win the competition, with Villas-Boas paying the price for an indifferent start to the Premier League after a big-spending summer.
They will start as favourites against Dnipro, who finished second in Group E behind Fiorentina, while Greek side PAOK or last season's runners-up Benfica lie in wait after the draw was also made for the last-16 in Nyon.
Swansea face a much more daunting route after being paired with Napoli, managed by former Liverpool and Chelsea boss Rafael Benitez.
The Swans, unlike Spurs, were unseeded for Monday's draw and knew they would be given tough opposition.
Michael Laudrup may feel his side have received the harshest possible draw, with Napoli still seething from their elimination from the Champions League last week.
The Serie A side won four of six games to sit alongside Borussia Dortmund and Arsenal but settled for third in Group F due to an inferior head-to-head record against their rivals.
Should Swansea cause an upset, they will face either Portuguese champions Porto or Eintracht Frankfurt.
Napoli's domestic rivals Juventus were pitted against Turkish club Trabzonspor, Spanish outfit Valencia face a tricky tie against Dynamo Kiev of Ukraine, while Real Betis have been drawn to face Russians Rubin Kazan in the other standout matches of the draw.
Europa League Round of 32 draw:
Dnipro v Spurs, Real Betis v Rubin Kazan, Swansea v Napoli, Juventus v Trabzonspor, Maribor v Sevilla, Viktoria Plzen v Shakhtar Donetsk, Chornomorets v Lyon, Lazio v Ludogorets, Esbjerg v Fiorentina, Ajax v RB Salzburg, Maccabi Tel-Aviv v Basel FC, Porto v Eintracht Frankfurt, Anzhi Makhachkala v Genk, Dynamo Kiev v Valencia, PAOK v Benfica, Slovan Liberec v AZ Alkmaar.
First legs to be played 20 February 2014.
Second legs to be played 27 February 2014.
Europa League Round of 16 draw:
Slovan Liberec/AZ v Anzhi Makhachkala/Genk, Lazio/Ludogorets v Dynamo Kiev/Valencia, FC Porto/Eintracht Frankfurt v Swansea/Napoli, Chornomorets/Lyon v Viktoira Plzen/Shakhtar Donetsk, Maribor/Sevilla v Real Betis/Rubin Kazan, Dnipro/Spurs v PAOK/Benfica, Maccabi Tel-Aviv/Basel v Ajax/RB Salzburg, Juventus/Trabzonspor v Esbjerg/Fiorentina.
First legs to be played 13 March, 2014.
Second legs to be played 20 March, 2014.