U.S. Treasury Secretary Steven Mnuchin told Trump in cabinet on Thursday that more sanctions were ready if Brunson were not freed.
A Chinese delegation led by Vice Minister of Commerce Wang Shouwen will meet USA representatives, China's Ministry of Commerce said in a statement, with the Wall Street Journal reporting that talks will take place in Washington on August 21 and 22. "Working with you, we have more that we're planning to do if they don't release him quickly".
A senior USA official told CNN that in exchange for Turkey's release of Brunson, Israel agreed to release Ebru Ozkan, a 27-year-old Turkish woman held in Israel on suspicion of aiding Hamas, the Palestinian militant group that controls Gaza.
"Any conversations we have with China to come up with a deal and any conversations we have with Mexico would be seen as a win for the U.S." said Jeffrey Frankel, president at Stuart Frankel & Co in NY.
Turkey's lira ended a three-day rally and slid as much as 8 per cent on Friday.
Turkey's president: US waging 'economic war' against Turkey
Against the dollar, the lira has lost 35 percent of its value this year, and Donald Trump announced new higher tariffs for Turkey amidst the tensions.
Doubts about Turkey's future intensified as relations with the United States, a longtime North Atlantic Treaty Organisation ally, soured.
Referring to Brunson, Trump said: "They have a great Christian pastor there, he's a very innocent man".
Finance Minister Berat Albayrak, Erdogan's son-in-law, told investors on Thursday that Turkey would emerge stronger from the currency crisis, insisting its banks were healthy and signalling it could ride out the dispute with Washington.
The United States has already imposed sanctions on two Turkish government ministers and doubled tariffs on Turkish steel and aluminum imports.
However, analysts are calling for a sharp hike in interest rates - which Erdogan adamantly opposes because it will put a brake on economic growth.
American officials have also protested the detentions of several Turkish employees of the US diplomatic mission in Turkey, including Metin Topuz, Hamza Ulucay and Mete Canturk. "They made a big mistake trying to tie this to other things". Turkish officials say the case is a matter for the courts.
However, there are still concerns over Turkish President Tayyip Erdogan's policies to combat the country's double-digit inflation and his row with Washington over detained American pastor Andrew Brunson.