All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
This narration was reported by Ibn Sa’d in at-Tabaqaat and by Ibn 'Asaakir in Taareekh Dimashq (the history of Damascus) with a wording similar to the one that you mentioned in the question.
Ibn Sa'd said:
“‘Abdullaah ibn Numayr reported from ‘Ubaydullaah, from Thaabit Al-Bunaani, from Anas ibn Maalik, who said, ‘The stomach of ‘Umar ibn Al-Khattaab rumbled from eating oil during the Year of Famine. He had forbidden himself clarified butter, so he tapped on his stomach with his finger and said, ‘We have nothing else for you until the people have the means of living.’’”
This narration has an authentic chain of narrators, as stated by Dr. Abdul Salaam ibn Mohsin Aal-Eesa in his book 'Diraasah Naqdiyyah fi Al-Marwiyyaat Al-Waaridah fi Shakhsiyyat ‘Umar ibn Al-Khattab wa Siyaasatihi Al-Idaariyyah Radhiya Allaahu ‘Anhu'.
The wording of Ibn Al-‘Asaakir is as follows:
“Ibn ‘Umar narrated that in the Year of Famine and when the people of Madeenah were very hungry, ‘Umar said, ‘I swear by Allaah, I will not eat bread with butter,’ and he did not like oil or barley or dates, but he liked butter, and he said, ‘I swear by Allaah, I will not eat bread with butter until Allaah provides for the Muslims in this present year.’ His face looked pale, and his stomach rumbled, and his strength weakened. His daughter bought a container of butter for him, but he swore by Allaah not to eat from it, so when he ate barley bread and dates without butter, his stomach rumbled, so, while he was in a meeting, he put his hand on his stomach and said, ‘Rumble or do not rumble, there is no butter for you until Allaah provides for the people.’”
However, we have not come across any scholar who judged its chain of narrators.
Allaah knows best.