Prospective fathers Lucas Neill and Josh Kennedy may play a role in Australia's two qualifiers against Iraq and Qatar later this month.
The two 2006 FIFA World Cup™ squad members were not included in Verbeek's 26-man travelling squad announced on Monday, but he said he has kept his options open for the pair to play against Iraq in Dubai on Saturday and Qatar in Doha on 14 June.
Both players' partners are expecting babies this month while striker Kennedy is also recovering from an ankle injury sustained in training with his German club Karlsruhe in April.
Verbeek told reporters on Monday before flying out to the Middle East that Kennedy may be used off the substitutes' bench against Iraq on Saturday.
West Ham defender Neill may join the Socceroos the day after the Iraq game, with his partner expecting to give birth to twins this week.
"We are also keeping a very close eye on Josh Kennedy because he's doing very well in his recovery," Verbeek said. "If you can have a player like him on the bench and he is almost fit and ready for 30 minutes, then I will look at this option.
"Lucas will be with us from Sunday - we're planning to let him come then. They expect the babies to come this week, but we don't want to put pressure on him and his wife. If he arrives on 8 June, he will have a week to prepare for the Qatar game and then the China game (in Sydney on 22 June)."
Verbeek said he named an enlarged squad as he was concerned that five of his players have a yellow card, as two cautions in the group matches means an automatic one-match ban.
Midfielders Vince Grella, Luke Wilkshire and Brett Holman, defender David Carney and goalkeeper Mark Schwarzer have all received yellow cards so far.
"With five yellow cards, worst-case scenario is we could miss five players in the game against Qatar," Verbeek said. "We think it's easier to have players already in the Middle East so they can get used to the climate."
Australia top their Asian qualifying group on seven points after Sunday's 1-0 win over Iraq in Brisbane. Iraq have just one point and must win on Saturday to stay alive in the group.
The top two in each group advance to the final stage of Asian Zone FIFA World Cup qualifying later this year.