Barnet are understood to be trying to land a friendly against Tottenham Hotspur as part of ex-keeper Lee Harrison's testimonial.
Harrison left Underhill with sacked boss Ian Hendon at the end of last month.
He has joined Dagenham & Redbridge as goalkeepinbg coach until the end of the season. The Daggers are currently in the League Two play-offs.
The Bees already have a match with Arsenal to look forward to, the annual Underhill clash due to take place on July 17. Home friendlies against Watford (July 21) and Charlton (July 24) have also been arranged.
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