The offer was made after Barcelona pulled off an astonishing result against Paris Saint-German in the Nou Camp.
Trailing 4-0 from the first leg, they bounced back to win 6-1 with three goals in the dying minutes.
In doing so, Barca became the first team to overturn a 4-0 first-leg deficit since the Champions League started in 1992-93 season.
But Dunfermline staged a similar great escape in the 1962-63 Fairs Cup.
The Pars, then managed by Jock Stein, lost 4-0 to Valencia in Spain in the first leg of the second round tie.
But on a pulsating night at East End Park they won the second leg 6-2 to level the tie on aggregate.
In the days before the away goals rule, a third match was staged in supposedly neutral Portual, and Valencia edged it 1-0.
Dunfermline tweeted the Catalan giants: “@FCBarcelona... congratulations guys.... fancy a friendly to say sorry for taking our record”.
There has been no response from Barcelona so far.