Ricardo Gareca's men suffered a 2-0 defeat to Chile in their most recent encounter, whereas Argentina had to settle for a 1-1 draw against Paraguay.
Gareca has earned plenty of plaudits during his time in charge of the Peru national team, but the 62-year-old is yet to steer his side to victory in qualification for Qatar 2022.
Peru proved no match for Chile on matchday three as they succumbed to a 2-0 defeat to their fellow World Cup hopefuls on Friday, with Arturo Vidal's double enough for Chile to take the spoils and leave Peru winless in the qualifying rounds.
Gareca has now gone over a year without leading Peru to a win in any competition, with the Bicolor's most recent triumph coming in a friendly against Brazil in September 2019 - a side they lost to 4-2 last month.
Peru will not take to the pitch in qualifying again for another four months following their showdown with Argentina, so Wednesday's hosts will no doubt be motivated to pull off a shock win as Gareca gears up to face his native country, with Venezuela and Bolivia the only two other sides without three points on the board so far.
In contrast, Argentina have made a strong start to their qualification campaign - as expected - but the South American powerhouses were held to a surprise draw by Paraguay on matchday three.
Angel Romero chalked up his third goal of qualifying from the penalty spot as Argentina fell behind early on, but Nicolas Gonzalez's header - set up by early substitute Giovani Lo Celso - ensured that Lionel Scaloni's men walked away with their unbeaten record still intact.
However, that one-pointer denied Argentina the chance to maintain their 100% start to proceedings, with La Albiceleste now two points behind early pacesetters Brazil heading into their final match of 2020.
Even without the presence of Paulo Dybala and Sergio Aguero, Argentina's famed attack still boasts some truly talented athletes in Lionel Messi, Lautaro Martinez, Angel di Maria and Lucas Ocampos, but goals have been hard to come by for Scaloni's side in qualifying.
Indeed, La Albiceleste have chalked up just four goals so far - the lowest in the top four - with bottom sides Venezuela and Bolivia the only two teams to have hit the back of the net on fewer occasions.
The most recent encounter between Peru and Argentina ended in a 0-0 stalemate, but the hosts have failed to beat La Albiceleste since 1997.
Peru World Cup Qualifying - South America form: DLL
Peru form (all competitions): LDLDLL
Argentina World Cup Qualifying - South America form: WWD
Argentina form (all competitions): WWDWWD
Peru have a couple more absentees to contend with for the visit of Argentina, with Carlos Zambrano already serving a ban after being sent off against Brazil.
Renato Tapia and Christofer Gonzales both picked up their second booking of qualification in the recent defeat to Chile, ruling the pair out of this encounter, while goalkeeper Pedro Gallese is doubtful.
Wilder Cartagena could therefore be tasked with occupying the defensive midfield role against the formidable attack of Argentina, while Pedro Aquino should start despite being taken off in the first half on Friday.
As for Argentina, Lo Celso came off the bench to bag an assist after Exequiel Palacios's horror injury - with the Bayer Leverkusen man fracturing a bone in his spine.
On a more positive note, Ajax left-back Nicolas Tagliafico is poised to make his return in defence for Argentina, which could see last week's goalscorer Gonzalez pushed further forward should Scaloni opt for a change up top.
Gonzalez will be battling Ocampos for a spot in the visitors' front three alongside Messi and Martinez, meaning that Di Maria will likely be restricted to an appearance from the bench once more.
Peru possible starting lineup:
Carvallo; Advincula, Araujo, Abram, Trauco; Cartagena; Carrillo, Aquino, Yotun, Flores; Lapadula
Argentina possible starting lineup:
Martinez; Montiel, Martinez Quarta, Otamendi, Tagliafico; Paredes, De Paul, Lo Celso; Messi, Martinez, Gonzalez
We say: Peru 1-3 Argentina
Peru have already shipped four goals to Brazil and are sure to be nervous at the prospect of facing an intimidating Argentina front line given their winless run. Scaloni's men did not have it all their own way against Paraguay but will be determined to round off the year on a high note, so all the signs are pointing towards a routine win for La Albiceleste on Wednesday.