The Seljuks were a bit concerned and were keeping an eye on things. They were interested in the crusade because it was originally intended for Egypt, and the Seljuks were also enemies of the Ayyubids who ruled Egypt and Syria at the time. But there was also a civil war among the Seljuks. The sultan had been deposed and was actually living in Constantinople when the crusade arrived.

Firstly, down in Egypt, the Ayyubid sultan al-Adil was aware of the situation. We don’t know his specific reaction but

"it is plausible to assume that al-Adil did consider the Latin conquest of Constantinople to be a dangerous development" (Kedar, pg. 103)

The crusade was supposed to attack Egypt directly but it had been diverted to Constantinople, and the crusaders ended up overthrowing the Empire and sacking the city. But in 1203-1204, the Egyptians and the crusader Kingdom of Jerusalem were both still expecting them to show up eventually. King Aimery of Jerusalem took the opportunity to attack the Nile delta with a fleet of ships, and al-Adil invaded Aimery’s territory. They agreed to a seven-year truce in September 1204.

Back in Constantinople, when the crusaders arrived in 1203, they received a request for help from the Seljuk sultan Kay Khusraw, who had been living there after being deposed by his brother. He thought both the crusaders and Byzantines might be able to help him out:

“‘Lords,’ said the sultan, ‘there is something I want to ask for you. I have a brother younger than myself who has taken from me by treason my land and seigniory of Konia, of which I was lord and of which I am the rightful heir. If you will help me recover my land and seigniory, I will give you right plentifully of my wealth, and will have myself baptized a Christian and all those who hold of me, if I can have again my seigniory with your help.’ And the barons answered that they would take counsel on it. So word was sent to the doge of Venice [Enrico Dandolo] and to the marquis [Boniface of Montferrat] and all the high barons, and they assembled in a great council, and finally it was their decision that they would not do what he sultan asked of them. And when they came from their council they answered the sultan that they could not what he asked of them, because they had still to get their reward from the emperor, and it would be dangerous to leave Constantinople, as things were then, and they dared not leave it. When the sultan heard this, he was very angry and went away again.” (Robert of Clari, pg. 78-79)

Kay Khusraw defeated his brother on his own and recovered his land and titles. Meanwhile, the crusaders destroyed the Byzantine Empire but several successor states sprung up, including one not far away in Nicaea. The Nicaean Byzantines were mostly focused on recovering Constantinople (which they eventually did, in 1261), but they also had to deal with attacks from their other neighbours, the Seljuks to the east. Kay Khusraw was killed in battle with Nicaea in 1211.

Kay Khusraw was succeeded by his son, Kaykhaus. A few years later, the Fifth Crusade was organized, and this time the crusaders did end up invading Ayyubid Egypt. Since the Seljuk sultanate also bordered on Ayyubid territories in Syria, both Kaykhaus and the crusaders thought it was in their best interests to ally against the Ayyubids. Kaykhaus attacked Aleppo in Syria while the crusaders were in Egypt but they never really managed to join together effectively.

So, the Seljuks reacted with interest when the Fourth Crusade arrived, mostly because the deposed sultan Kay Khusraw thought it was a good opportunity to reclaim his throne. But it backfired for him, because was killed in combat with the remnant Byzantine state in Nicaea. They didn't have much direct contact with the crusaders in Constantinople because Nicaea was in the way. But now that they were in contact with western crusaders, the Seljuks tried to ally with them against their common enemy, the Ayyubids.

Sources:

Jonathan Phillips, The Fourth Crusade and the Sack of Constantinople (Pimlico Press, 2005)

Benjamin Z. Kedar, “The Fourth Crusade's second front", in Angeliki E. Laiou, ed., Urbs Capta: The Fourth Crusade and its Consequences

Robert of Clari, The Conquest of Constantinople, trans. Edgar Holmes McNeal (Columbia University Press, 1936)

James M. Powell, Anatomy of a Crusade: 1213-1221 (University of Pennsylvania Press, 1986)