According to the Islamic and Quranic teachings, the Prophets and infallible Imams (A) have access to the knowledge of unseen and it is possible for the Prophets and their infallible successors to acquire such a knowledge.
In the Qur’an, God is referred to as the Knower of both the Seen and the Unseen (6:73; 9:94, 105; 13:9;32:6; 39:46; 59:22; 62:8; 64:18; 72:26:27; 34:3). It means that He has the knowledge of all what exist in both this world and the Hereafter. God states that some specific group of people, namely the prophets are allowed to have a limited access, through revelation, to God’s knowledge; because their loyalty was approved.[1] The Qur’an affirms this limited access:” … Had I knowledge of the unseen, I would have acquired much good, and no evil would have touched me...”[2] According to one report, which historically confirms such limited access, the Prophet’s answer was no to some of the Quraysh who asked him if God had informed him about the time of rising and falling prices, that they might benefit from this information in their mercantile activity.[3] Although, these verses refute other’s access to God’s Knowledge except the prophets, but both Shiite and Sunni generally accept the reality of “lesser Miracles”, which are known as Keramat. Shiite believes that their infallible Imams have such a limited access to God’s Knowledge as well. [4]
[1] Chapter 72, verse 26-27. ...عَالِمُ الْغَيبِ فَلَا يظْهِرُ عَلَى غَيبِهِ أَحَدًا- إِلَّا مَنِ ارْتَضَى مِنْ رَسُولٍ
[2] Chapter 7, verse 188. ...قُلْ لَا أَمْلِكُ لِنَفْسِي نَفْعًا وَلَا ضَرًّا إِلَّا مَا شَاءَ اللَّهُ وَلَوْ كُنْتُ أَعْلَمُ الْغَيبَ لَاسْتَكْثَرْتُ مِنَ الْخَيرِ وَمَا مَسَّنِي السُّوءُ
[3] See: The Study of The Qur'an, Seyed Hussein Nasr, see the description of 72:16-17
[4] See: The Study of The Qur'an, Seyed Hussein Nasr, see the description of 7:188