The pair currently sit in joint-ninth place with 88 caps each, three short of Niall Quinn in eighth position.
The 35-year-old played in the previous international break, starting and finishing the 1-1 draw with Switzerland.
Tynecastle boss Craig Levein said last week that one of the motivating factors for the former Aston Villa and Stoke City midfielder coming to Scotland was a desire to remain in the Irish national team set-up under coach Mick McCarthy.
Levein told the Evening News: "Part of him coming here was that he still had that short-term focus, that he’s determined to get to the Euros and to do that he needs to be playing regularly and playing well. Thankfully he chose us to come and do that."
Whelan is hopeful of making it to his fourth international tournament, having been included in the Ireland squad for the 2012 and 2016 European Championship as well as the 2014 World Cup.