It is part of the Sunnah to turn one’s face towards the khateeb and look at him
Question

During the Friday khutbah, some of the worshippers look at the khateeb; some look straight ahead; some look at the ground; and some close their eyes. Is there a specific Sunnah regarding this matter?
Praise be to Allah.It was narrated in a saheeh hadeeth that one of the companions of the Prophet (peace and blessings of Allah be upon him) said: when the Prophet (peace and blessings of Allah be upon him) mounted the minbar, we would turn our faces towards him.
(al-Silsilat al_Saheehah by al-Albani, no. 2080) 
It was narrated that Abaan ibn ‘Abd-Allah al-Bajili said: I saw ‘Udayy ibn Thaabit turning to face the imam when he stood to deliver the khutbah. I said to him, I saw you turn your face towards the imam. He said, I saw the Companions of the Prophet (peace and blessings of Allah be upon him) doing that. 
It was narrated that ‘Abd-Allah ibn Mas’ood said: when the Messenger of Allah (peace and blessings of Allah be upon him) mounted the minbar, we would turn our faces towards him him. This was narrated by al-Tirmidhi, who said, in the same chapter there are reports narrated from Ibn ‘Umar and Muhammad ibn al-Fadl. According to the scholars among the companions of the Prophet (peace and blessings of Allah be upon him) and others, this is to be followed. They regard it as mustahabb to turn to face the imam when he delivers the khutbah. This is the view of Sufyaan al-Thawri, al-Shaafa’i, Ahmad and Ishaaq. 
It was narrated that Yahyaa ibn Sa’eed al-Ansaari said: “The Sunnah when the imam sits on the minbar on Friday is for all the people to turn their faces towards him.” 
It was narrated from Naafi’ that Ibn ‘Umar used to finish his tasbeeh before the imam came out; when he came out, he would turn to face him before the imam even sat down. 
Al-Albani (may Allah have mercy on him) compiled these ahaadeeth in al-Silsilat al-Saheehah, no. 2080, and commented on them. 
It was narrated that Abu Sa’eed al-Khudri (may Allah be pleased with him) said: “The Messenger of Allah (peace and blessings of Allah be upon him) sat on the minbar and we sat around him.” (Narrated by al-Bukhaari, 921)
Al-Bukhaari narrated the hadeeth in “Chapter: The imam facing the people, and the people turning their faces towards the imam when he delivers the khutbah, and Ibn ‘Umar and Anas (may Allah be pleased with them) turning their faces towards the imam.” 
The point of the hadeeth is that the fact that they sat around him to listen to his words implies that they were looking at him in most cases. This is not affected by what was said earlier about the khateeb standing during the khutbah, because this implies that he used to speak whilst he was sitting in a high place and they were sitting at a lower point. If that was the case at times other than the khutbah, then it is more appropriate to do that at the time of the khutbah because there is the command to listen to it attentively.   
He said: 
“One of the reasons for their turning their faces towards the imam is to facilitate their listening to his words, and to observe good manners when listening to him. If a person turn his face towards him with the proper physical posture and a focused mind, that will better enable them to understand his preaching and is in accordance with the reason why the khateeb is commanded to stand.” 
And Allah knows best.