We could not find any trance of this phrase in the hadîth literature. We could not even find it in any of the compilations the preserve the saying of the Companions and Successors.
We believe this is just an old wise saying. The meaning of this statement is sound. The Qur’ân and Sunnah come with numerous encouragements for seeking knowledge at all times and in all beneficial fields, whatever the age of the person.
Allah says: “But say: “O my Lord! Increase me in knowledge”.
The Prophet (peace be upon him) said: “Whoever seeks a way to acquire knowledge Allah will make easy his way to Paradise.” [Sahîh Muslim (2699)]
It was also related by Anas b. Malik that the Prophet (peace be upon him) said: “Seeking knowledge is obligatory upon every Muslim.” [Sunan Ibn Mâjah (224) and others]
Imam Ahmad b. Hanbal had said: “We will accompany the inkpot until our death.”
And Allah knows best.