Dhindsa and Gujral (the son of former Prime Minister I K Gujral), both senior leaders of SAD, filed their nomination papers here, a state Assembly spokesman said.
The term of five members of Rajya Sabha elected from Punjab will expire in April.
The polling for electing five new RS members will be held on March 21.
The MPs whose term is expiring are Ashwani Kumar (Cong), Avinash Rai Khanna (BJP), Sukhdev Singh Dhindsa (Akali Dal), Manohar Singh (Cong) and Naresh Gujral (Akali Dal).
Former Punjab Congress chief Partap Singh Bajwa, former CLP leader Sunil Kumar Jakhar, senior party leaders S S Dullo and Laal Singh are among the front-runners as Congress candidates. BJP is likely to field cricketer-turned-politician and former MP Navjot Singh Sidhu for Rajya Sabha.