Is it permissible for an employee to read Qur’aan during work hours?

If that is at the company’s expense – as mentioned in the question – then it is not permissible, because the employee has agreed with the workplace that he will do the work that he is entrusted with, adhering to the daily work hours. So if he does not work complete hours, or falls short in his work, that is forbidden, because Allaah says (interpretation of the meaning): 

“O you who believe! Fulfil (your) obligations”

[al-Maa’idah 5:1]

And the Prophet (peace and blessings of Allaah be upon him) said: “The Muslims are bound by their conditions.” Narrated by Abu Dawood (3594), classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

But if his reading Qur’aan does not affect his work performance, there is nothing wrong with that in sha Allaah. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: If an employee has finished his work and he wants to make use of the time by reading Qur’aan or reading something useful, or even wants to take a nap so that he can rest a little, is there anything wrong with that? 

He replied: 

There is nothing wrong with that so long as he has completed the work that he was entrusted with. But if he is negligent or falls short in doing his work, then it is haraam for him and it is not permissible. As for taking a nap, there is no concession with regard to that, because he will have no control over himself and he may sleep and miss his work without realizing. End quote from Fataawa al-Huqooq, compiled by Abu Khaalid al-Juraysi, p. 59. 

See also the answer to Question no. 9374. 

And Allaah knows best.