Syria today maintained official silence but dropped cautious hints that President Hafez Assad is trying to solve the American hostage crisis in Beirut within a matter of days.

As diplomats here credited Syria with inspiring the offer by Nabih Berri, the Amal militia leader negotiating for the hijackers, to transfer the hostages to a western embassy in Beirut or to Syria, a pattern of seemingly unconnected and all but imperceptible signs pointed toward growing Syrian determination.

Quoting Syrian sources, diplomats here reported that Berri has been in Damascus incognito once -- and perhaps twice -- in the past few days to confer with Syrian officials and presumably hammer out the offer he unveiled in Beirut at midday. [In Washington, U.S. officials also said they believed Berri had made secret trips to the Syrian capital recently.]

And the official Syrian news agency announced that President Assad will leave for a recently delayed official visit to Czechoslovakia "within the next few days."

Diplomats and analysts reasoned that Assad, said to be following the hostage crisis with his legendary attention to detail, would not risk failure by setting off for Prague unless a solution has been found.

Furthermore, diplomats said they sensed a new desire to end the crisis quickly in their dealings with their Syrian contacts. Quite apart from the hostage situation, Syria is all but isolated in the Arab world because of its role in helping Amal attack the Palestinian refugee camps in Beirut.

Also considered signficant were recurring rumors that Syria now was determined to crack down hard on the pro-Iranian Hezbollah, or radical fundamentalist Shiite Moslem Party of God, believed responsible for seizing the hostages aboard the TWA airliner hijacked at Athens airport 13 days ago.

Officially, advisers at the presidency, where the crisis is being closely monitored, uncharacteristically invoked the confidentiality of developments -- rather than issuing a curt no comment -- to justify their refusal to discuss Berri's offer.

That, Syrians and diplomats alike agreed, was in keeping with Assad's longstanding insistence on prudence, even if in this crisis the officials acknowledged their concern.

Despite Syria's apparent desire to end the hostage stalemate, Assad has a well-deserved and documented reputation for never tipping his hand until deals are signed, sealed and delivered.

And no responsible analyst here assumes that even as determined and effective a leader as Assad can overcome easily the murky uncertainties of Lebanon's reigning anarchy and solve the hostage crisis with the wave of a magic wand.

Moving the hostages to a western embassy as Berri suggested -- and the French Embassy he mentioned has spacious grounds and houses capable of sheltering them -- would solve the problem of their personal safety by removing them from their erratic captors, according to diplomats.

But it would not restore their freedom of movement, as President Reagan has insisted must be done, at least not until Israel released the predominantly Lebanese Shiite prisoners it holds at Atlit.

That analysis prompted diplomatic speculation here that Assad favored Berri's alternate suggestion involving moving the hostages to Syria. The offer was conditioned on the hostages remaining in the care of either a western embassy or Syria pending Israeli release of the Atlit prisoners.

But at face value, diplomats doubted Assad could honor that part of the bargain without laying himself open to charges that Syria was conniving in the hijacking he is known to have denounced.

Yet, such a transfer here would help save Berri's face by shifting responsibility to Assad. Berri would not be seen as surrendering the hostages to the United States, but to his ally and protector in Damascus.

Theoretically, Syria as a sovereign state could order the transferred hostages' unconditional release by invoking the higher interests of the state.

Logically, Syria would want to keep the hostages on its soil the shortest possible time.

If Syria released the hostages without obtaining the simultaneous release of the Atlit prisoners Berri would look foolish.

But diplomats argue that Berri could hardly afford to dispute anything his Syrian ally and protector chose to do if no other face-saving compromise could be arranged.

Also unclear is what Israel would be willing to do to help Syria accomplish what the Reagan administration demands -- the hostages' unconditional release.