The German coach, whose deal at the Commerzbank-Arena expires at the end of the season, led Frankfurt to a spot in the UEFA Europa League last term with a sixth-placed finish in the Bundesliga.
Frankfurt have struggled to replicate that form this campaign, and sit just one point above the relegation play-off place in 15th having taken just three wins from 17 games.
However, Frankfurt topped Group F in the Europa League, winning five out of six matches to earn a last-32 clash with Portuguese side Porto next month.
And, despite their poor domestic form, Frankfurt's executive chairman Heribert Bruchhagen is hopeful Veh will remain with the club beyond the end of the season.
"Armin can extend his contract at any time," Bruchhagen told Sky Sport HD.
"He has the right to make his own decision about his professional future.
"Armin knows that everyone at Frankfurt would like him to extend his contract."
Frankfurt resume Bundesliga action on Saturday with a home game against Hertha Berlin.
