Some people hold that it is impermissible to conclude a marriage contract or consummate marriage during the sacred months or on other specific times; does this claim have any basis in the sharia?
Please, reply soon, because someone I know is planning to conclude his marriage contract within few days.

All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Arguing that it is impermissible to conclude a marriage contract or consummate marriage during the sacred months or any other specific times is making a false claim. There is no origin for such claims in the Islamic sharia. This claim could be traced back to pre-Islamic Arabian customs. Arabs used to see an evil omen in a marriage that would take place during the month of Shawwaal. Therefore, ‘Aa’ishah said, "The Prophet, sallallaahu ‘alayhi wa sallam, consummated his marriage with me in the month of Shawwaal, in which you see an evil omen for getting married!"

Arabs used to have bad omens concerning the month of Safar and some specific days, such as Wednesday. Islam, however, abolished all forms of superstitious belief in bad omens and considered them acts of shirk (polytheism). The Prophet, sallallaahu ‘alayhi wa sallam, warned against superstitious belief in evil omens and pessimism. Abu Hurayrah reported that the Prophet, sallallaahu ‘alayhi wa sallam, said: "(There is) no bad omen (from birds), nor is there any haamah (old Arab superstitious belief), nor is there any bad omen in the month of Safar..."

Hence, it is permissible to conclude a marriage contract at any time of the year, except when the person is in a state of ihram (i.e. ritual consecration), in which case, he has to end his state of ihram first.

Allah Knows best.