One of the rulings of sharia which is aimed at cutting off all possible fitnah, blocking all means that may lead to shirk and closing the door to exaggeration is the prohibition on taking graves as places of worship, or praying facing towards them, or taking graveyards as a place of prayer.
There is no differentiation in that between graves of Muslims or graves of mushrikeen; in fact with regard to the graves of Muslims and righteous people, it is more important to keep away from them, because shirk and fitnah are more likely concerning them.
Al-Bukhaari (436) and Muslim (531) narrated that 'Aa'ishah and ‘Abd-Allaah ibn ‘Abbaas (may Allaah be pleased with him) said: When the Messenger of Allaah (peace and blessings of Allaah be upon him) was dying, he drew the blanket over his face, then when the pains of death grew too intense, he uncovered his face and said: “May Allaah curse the Jews and the Christians; they took the graves of their Prophets as places of worship,” warning against doing what they had done.
And it was narrated that Abu Sa’eed al-Khudri (may Allaah be pleased with him) said: The Messenger of Allaah (blessings and peace of Allaah be upon him) said: “All the Earth is a mosque except graveyards and washrooms.”
Narrated by Imam Ahmad (11379), Abu Dawood (492) and al-Tirmidhi (317). Classed as saheeh by al-Haakim, and al-Dhahabi agreed with him. Shaykh al-Islam Ibn Taymiyah classed its isnaad as jayyid, but al-Daraqutni and al-Tirmidhi thought it most likely to be mursal.
And there are many well-known hadeeths about this matter.
Ibn al-Qayyim (may Allaah have mercy on him) said concerning the lessons learned from the battle of Tabook and what is mentioned in it of Masjid al-Diraar, which Allaah forbade His Prophet (blessings and peace of Allaah be upon him) from praying in:
[One of the lessons we learn]: is that a waqf is not valid if it involves something other than an act of righteousness or of worship, just as the waqf for this mosque [meaning Masjid al-Diraar] was not valid. Based on this, a mosque is to be demolished if it is built over a grave, and the deceased is to be exhumed if he is buried inside a mosque. This was stated by Imam Ahmad and others.
A mosque and a grave cannot be combined in the religion of Islam, rather whichever one of them comes after the other should be prevented; the ruling favours the one that was there first. If they are built at the same time, that is not permissible, and this waqf is not valid and is not permissible, and it is not valid to pray in this mosque, because the Messenger of Allaah (blessings and peace of Allaah be upon him) forbade that, and cursed those who take graves as mosques or who set up lamps over them.
This is the religion of Islam with which Allaah sent His Messenger and Prophet, but it has become as a stranger among the people, as you see! End quote.
Zaad al-Ma’aad fi Huda Khayr il-‘Abaad (3/572)
But if the graves or graveyard are close to the place where it is intended to build a mosque, there is nothing wrong with building a mosque, subject to 3 conditions:
1.That the mosque should not be built with the aim of venerating those graves or seeking blessing from them.
2.That the graves should not be in the direction of the qiblah of the mosque, because of the hadeeth of Abu Marthad al-Ghanawi (may Allaah be pleased with him), according to which the Messenger of Allaah (blessings and peace of Allaah be upon him) said: “Do not sit on graves and do not pray towards them.” narrated by Muslim, number 972.
3.The mosque should be separated from them in a clear manner, so that these graves will not form any part of the halls or courtyard of the mosque, and so that it will clearly appear to the onlooker that the mosque is completely separate from the graves, such as a path, a road, a large open space or the like.
Abu Bakr al-Athram said: I heard Abu ‘Abd-Allaah – meaning Ahmad ibn Hanbal (may Allaah have mercy on him) – when he was asked about praying in graveyards. He disapproved of prayer in graveyards. It was said to him: The mosque is among the graves, can I pray in it? And he disapproved of that. It was said to him: It is a mosque and between it and the graves there is a barrier. He disapproved of offering obligatory prayers therein, but he granted a concession with regard to offering funeral prayers there, and he mentioned the hadeeth of Abu Marthad al-Ghanawi (may Allaah be pleased with him), according to which the Prophet (blessings and peace of Allaah be upon him) said: “Do not pray towards graves.” He said: Its isnaad is jayyid. End quote. Fath al-Baari by Ibn Rajab, 2/398.
There is no reason why a mosque cannot be built in an area close to the graveyards of mushrikeen -- or of Muslims -- on condition that the mosque is not within the boundary of the graveyard, rather it should be clearly separated from it by a path or the like.
But if it is possible for you to find another place, far away from the graveyard, that is better and is more on the safe side lest any expansion of the graveyard, with the passage of time, reach the boundaries of the mosque.
And Allaah knows best.