Meanwhile, the home side welcome the leaders to De Grolsch Veste having recorded three wins from five matches, a run which has kept the club in contention for the top five.
Given Ajax's recent dominance of the domestic scene, recording two successive draws feels like a considerable setback for everyone associated with the Dutch giants.
However, including the defeat to Twente before Christmas, it leaves Erik ten Hag with genuine questions to answer regarding his side's form.
On the positive side, a stirring comeback which involved new signing Sebastien Haller secured a 2-2 draw with rivals PSV Eindhoven at the weekend.
Nevertheless, the bigger picture shows Ajax conceding seven goals in their last five top flight games when PSV and Feyenoord have been closing the gap at the top.
With Feyenoord to come on Sunday, Ten Hag and his players are aware that they could soon find themselves in third place if they do not improve at the back over their next two matches.
Having only suffered defeat to Twente as recently as December 5, they will also be motivated to ensure that their next opponents do not record a rare double.
Twente have endured an indifferent period since their shock win in Amsterdam, losing home matches to AZ Alkmaar and Sparta Rotterdam and winning on their travels against VVV-Venlo and Emmen.
Ron Jans has been left frustrated by the inconsistencies of a squad who have suggested on occasions that they should be sitting higher than their current sixth position.
They have now gone four matches without recording a home victory in the Eredivisie, a period stretching all the way back to October 31.
FC Twente Eredivisie form: LWLWLW
Ajax Eredivisie form: WLWWDD
Ajax form (all competitions): LWWWDD
Haller is in line to make his first start for Ajax, taking the place of Zakaria Labyad in attack.
Having taken the opportunity to rest players during the closing stages of the 4-1 win at Emmen, Jans could opt to select the same starting lineup.
FC Twente possible starting lineup:
Drommel; Ebuehi, Pleguezuelo, Pierie, Oosterwolde; Roemeratoe, Zerrouki, Bosch; Cerny, Danilo, Menig
Ajax possible starting lineup:
Onana; Mazraoui, Schuurs, Blind, Tagliafico; Alvarez, Gravenberch; Antony, Klaassen, Tadic; Haller
We say: FC Twente 1-2 Ajax
While Twente will be confident of extending Ajax's winless streak, they will also be aware that the leaders will be determined to retain hold of first place. With that in mind, we expect the visitors to battle their way to a hard-earned three points at De Grolsch Veste.