All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
As long as those shorts cover the ‘Awrah (i.e. body parts that should be covered as per the Sharee‘ah) of the man, which is the area between the navel and the knee, then there is no harm in wearing them, unless wearing such shorts constitutes imitation of the disbelievers or people of bad moral character, in which case it is forbidden to wear them so as not to imitate disbelievers and people of bad moral character. The knee itself is not part of the ‘Awrah. For more benefit, please refer to Fataawa 84742 and 3882.
What you have mentioned of part of the thigh possibly being uncovered when running or jumping is not enough to deem wearing such shorts forbidden because it is possible that nothing of that shows. If it does show without intention, then you bear no sin for that. The gown of the Prophet, sallallaahu ‘alayhi wa sallam, was withdrawn from his thigh when he was on horseback, so Anas said: “and the gown of the Prophet of Allaah, sallallaahu ‘alayhi wa sallam, was withdrawn from his thigh and I could see the whiteness of his thigh.” [Al-Bukhari and Muslim]
Some scholars held that the man’s thigh is not included in the ‘Awrah in the first place, especially the lower part of the thigh near the knee.
Al-Mawsoo‘ah Al-Fiqhiyyah (Kuwaiti Encyclopedia of Jurisprudence) reads, “A group of scholars maintained that the man’s thigh is not included in the ‘Awrah, among them ‘Atta’, Daawood, Muhammad ibn Jareer, and Abu Sa‘eed Al-Istakhri from the Shaafi‘i School. This is also one of the opinions reported from Imaam Ahmad. They relied on the Hadeeth reported by ‘Aa’ishah in which she says: “The Prophet, sallallaahu ‘alayhi wa sallam, was lying down in my room with his thighs - or his shanks - uncovered, and Abu Bakr sought permission to enter. He let him in and remained in the same state (with his thighs uncovered) and they talked. Then, ‘Umar sought permission to enter and it was given to him and he remained as he was. Then, ‘Uthmaan sought permission to enter, so the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, sat up and straightened his clothes.” When she later asked him about it, he, sallallaahu ‘alayhi wa sallam, said: “Should I not be bashful before a man before whom the Angels are bashful.” [End of quote]
The opinion adopted in Islamweb is that the man’s thigh is included in the ‘Awrah and this is the opinion of the majority of scholars. However, we mentioned the opposing opinion to clarify that this matter was subject to different scholarly opinions, so there is no need for making it difficult for people by deeming it impermissible to wear what reaches down to the knee for fear that something may be exposed when jumping.
Having said that, there is no doubt though that it is more prudent for the man to wear something underneath such shorts to conceal his ‘Awrah properly.
Allaah Knows best.