The Culture Media and Sport (CMS) select committee may also seek the FA chairman's views on world governing body Fifa's president Sepp Blatter.
Sunday Times journalists Heidi Blake and Jonathan Calvert will also give evidence on Tuesday.
In June, the newspaper published allegations of bribery and corruption concerning Qatar's winning bid,.
Fifa are thought to have been invited but has confirmed it will not send a representative.
The UK newspaper obtained millions of secret documents - emails, letters and bank transfers - which it alleges are proof that the disgraced Qatari football official Mohamed Bin Hammam made payments totalling US$5m (£3m) to football officials in return for their support for the Qatar bid.
The FA chairman has been increasingly outspoken about Fifa in recent weeks, telling The Guardian: "I think the cult of Blatter is pathetic, I don't think it's what it should be about."
Dyke has previously stated that he would back a re-vote if allegations of corruption are proven, telling BBC Sport in June: "I think if it is shown it was a corrupt system and that the people who won bribes and other influences to get the vote, then of course it has got to be done again."
Fifa's ethics investigator, Michael Garcia, is finalising his report into how both the 2018 and 2022 World Cups were awarded and is likely to hand it over to Fifa's ethics adjudicator, Hans-Joachim Eckert, at the end of July.
Sources close to the investigation say Eckert, a senior German judge, will then take six to eight weeks to reach a decision on whether any individuals under Fifa's jurisdiction should face sanctions.
He does not have the power to strip Qatar of the World Cup, with any decision over a potential re-vote a matter reserved for Fifa's executive committee.
The organisers of the Qatar World Cup have consistently denied any wrongdoing.
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