Szmodics was named in the Ireland squad for two summer internationals, but had to pull out after aggravating a shoulder injury.
And Taylor would have had a great chance of making that squad, but for suffering a hamstring injury in the penultimate game of last season.
Injury and a lack of gametime ruled both of them out of Ireland’s matches in the current international break.
The last player to win a full international cap while playing for Posh was right-back Michael Smith for Northern Ireland in 2016.
Gaby Zakuani’s 20 caps for DR Congo is the most by a serving Posh player.
Here are the Posh internationals...
1. GABY ZAKUANI
Zakuani (right) 20 caps for DR Congo. Iron man centre-back who played in three Africa Cup of Nations for his country. Made over 250 appearances for Posh and helped them to two promotions to the Championship. Now managing Spalding United. Photo ISSOUF SANOGO/AFP via Getty Images.
2. CRAIG MORGAN
19 caps for Wales. Steady centre-back who helped Posh to back-to-back promotions into the Championship under Darren Ferguson. Good on the ball and a decent all-round defender who won 23 Welsh caps in total. Photo: Richard Heathcote/Getty Images.
3. JAMES QUINN
11 caps for Northern Ireland. The lesser of two Northern Irish forwards named Quinn who played for Posh. Made 50 international appearances in total including in a famous 1-0 World Cup qualifying win over England when he was at Posh. Photo by Ian Walton/Getty Images.
4. GRANT McCANN
9 caps for Northern Ireland. A midfield maestro and a star of the Posh promotion-winning team of 2010-11. Managed Posh less successfully, but steered Hull to the League One title.