* Outbound deals rise for 3rd straight month but for low levels
* Belt and Road investments up 50 pct
* Speculation growing that Beijing may relax capital curbs
* Capital outflows, yuan depreciation seen under control
* Yuan has gained 4 pct so far this year, 6.8 pct in 2017 (Adds detail)
BEIJING, Feb 13 (Reuters) - China's non-financial outbound direct investment rose nearly 40 percent in January from a year earlier, in the latest sign that Beijing may be slowly relaxing tough foreign exchange controls as the government grows less worried about capital flight.
While the total in dollar terms was modest at $10.8 billion, the data marked the third straight month that China's outbound investment has rebounded after regulators' year-long battle against what they see as "irrational overseas spending."
Last week, sources told Reuters that China has revived an outbound investment scheme after a two-year suspension, allowing foreign fund managers to raise money domestically and invest it offshore.
Official data the same week showed China's foreign exchange reserves rose for the 12th month in a row in January as the yuan (renminbi) currency continued to rally, while the forex regulator said cross-border capital flows are becoming more balanced.
"In limited but noticeable steps, Chinese authorities are... tweaking knobs on capital controls to permit some more outflows," Bank of Tokyo-Mitsubishi UFJ analysts Jackit Wong and Cliff Tan said in a Feb. 8 research note.
The subtle shift may signal authorities are growing increasingly uncomfortable with the pace of gains in the yuan so far this year, they said.
The currency has appreciated 4 percent against the U.S. dollar so far in 2018 after rising 6.8 percent last year, its first gain in four years. The sharp rise has fueled worries that it could erode China's export competitiveness.
The January rise in outbound investment reported by the Ministry of Commerce on Tuesday compares with a 35.7 percent decline in ODI last January.
For all of 2017, China's overseas investment tumbled 29.7 percent as Beijing clamped down on capital leaving the country, the first decline on record after years of growth.
Outbound deals last year totalled $120.08 billion.
Amid tighter regulatory scrutiny, Chinese firms scrapped a number of foreign acquisitions over the past year, including a $1 billion deal to fund film production at Viacom Inc's Paramount Pictures that was canceled in November.
China says it continues to encourage genuine overseas deals but has vowed to limit investment in overseas property, hotels, entertainment, sports clubs and film industries it suspects is more speculative and aimed at evading capital controls.
There were no new deals in the property, sports or entertainment sectors in January, the Ministry of Commerce said.
Investments related to China's "Belt and Road" initiative rose 50 percent on-year in January to $1.23 billion, though Belt and Road deals only accounted for 11.4 percent of total ODI, down from 12 percent for last year overall.
The initiative is aimed at building a modern-day 'silk road' trade route from China across Southeast Asia and beyond to the Middle East, Europe and Africa. (Reporting by Elias Glenn and Beijing Monitoring Desk; Editing by Kim Coghill)