No, they never met in person, they only communicated through ambassadors. I thought I had written about this before but actually I only mentioned it in passing in a couple of other answers (What did Saladin think of Richard the Lionheart and Baldwin IV? and Did Saladin and Richard I ever communicate with each other after the Third Crusade ended?), so I'll piece them together into one answer here:

Richard sent ambassadors to Saladin as soon as he arrived on the Third Crusade in 1191. Richard wanted to meet with him in person, but Saladin couldn’t agree. He was concerned that two kings meeting in person might hastily agree to things that couldn’t work in reality, and then it would be awkward to fight against each other afterwards when war would inevitably break out again. They didn’t speak the same language, and Saladin felt it was inappropriate to communicate with another king through an interpreter.

These kind of sound like lame excuses though; what Saladin probably really meant was that it was extremely presumptuous for Richard to assume he was in any position to dare communicate with Saladin directly. Saladin had conquered almost the entire crusader kingdom and the Third Crusade only held a tiny foothold around the city of Acre, and in Tyre. He could recognize Richard as a fellow king, but certainly not that they had equal standing.

The crusaders' position did improve though once they recovered Acre and the rest of the coastline. So for the rest of Richard's stay in the east in 1191 and 1192 they did communicate frequently. Richard used the local crusader nobility that had grown up in the east since the time of the First Crusade; nobles like Humphrey of Toron spoke Arabic and French. Humphrey could act as an ambassador to Saladin, and translate what Saladin's ambassador's were saying to Richard.

Sometimes one of Saladin's ambassador's was his brother al-Adil (known in crusader sources as “Saphadin”, from his honorific title Sayf ad-Din). This was probably a high honour and a sign of Saladin's increasing respect for Richard. However, both al-Adil and Saladin considered Richard a bit untrustworthy and treacherous. For example there is the famous story that Richard wanted al-Adil to marry his sister Joan, and the two could rule a joint Christian-Muslim kingdom in Jerusalem. The story is only found in the Muslim sources though, so we’re not entirely sure what happened from the crusader viewpoint. Saladin thought the offer

“was intended to mock and deceive him.” (Baha ad-Din, pg. 188)

Saladin was also annoyed that Richard wanted Jerusalem back - both sides knew that Richard couldn't take it by force, but Richard kept asking Saladin to give it back anyway, something he must have known Saladin could never do. During the Siege of Acre in 1191, Richard massacred about 3000 Muslim prisoners, possibly because he just couldn’t afford to feed all those extra hungry mouths. Saladin was furious, and he felt he had no choice but to execute his own Christian prisoners.

Near the end of the crusade in 1192, Richard was often sick (probably with malaria), and

“...there was a steady stream of emissaries from the king of England requesting fruit and ice. In his illness God had burdened him with a yearning for pears and plums...” (Baha ad-Din, 227-228)

On other occasions Richard's ambassadors asked for “fruit and ice”. But Baha ad-Din also notes that whenever messengers and ambassadors were travelling back and forth, it was a great opportunity to spy on troop movements and numbers, which the crusaders were apparently happy to chat about openly.

So, they never met in person, and negotiations during the crusade and for the peace treaty at the end were conducted through ambassadors. Richard often sent messengers but Saladin believed he was always stalling in order to recuperate his forces; and Saladin often sent messengers but they were always collecting intelligence at the same time. Their supposedly friendly and respectful relationship is more an invention of modern romance, such as the novels of Walter Scott.

Sources:

Baha' al-Din ibn Shaddad, The Rare and Excellent History of Saladin, trans. Donald S. Richards (Ashgate, 2002)

The Chronicle of Ibn al-Athir for the Crusading Period, trans. Donald S. Richards, part 2 (Ashgate, 2007)

John Gillingham, Richard I (Yale University Press, 1999)

Jonathan Phillips, The Life and Legend of the Sultan Saladin (Yale University Press, 2019)

M.C. Lyons and D.E.P. Jackson, Saladin: The Politics of the Holy War (Cambridge University Press, 1984)