'Gerlinde is today (Tuesday) climbing her 13th peak, which is the 8,611-metre Himalayan peak of K-2, and if she manages to do that, she might join Oh in the record,' he told DPA.
Oh was quoted as saying that the 8,091-metre Annapurna, the only one of the 14 mountains she has not climbed, is her next goal.
She had postponed her climb to mourn the death of her rival Ko Mi-Young.
Oh is due to return home in mid-August and decide whether to tackle Annapurna this autumn or next spring, the Black Yak clothing company was quoted as saying by Yonhap.
In 1999, South Korean Ji Hyung Ok died while descending after summitting Annapurna. Oh and Ko had promised to attempt Annapurna together on the 10th anniversary of Ji's death.