"suggesting that the process" is correct and usable in written English.
You can use this phrase when you are attempting to point out an idea or possible course of action. For example, "The data we have collected is suggestive of a longer timeline, suggesting that the process should take at least six months."
Mr. Brian chatted on, suggesting that the process of buying a used car was similar to buying an antique.
The oldest-established group (Afro-Caribbeans) are the most integrated, suggesting that the process has been going on for some time.
It had strangely few imitators, suggesting that the process of discarding convention and using the evidence of the eye is a slow one.
Your comments, and those of some members of parliament, have at a minimum undermined the perception of impartiality by suggesting that the process is being driven by political rather than legal concerns".
The choice of hashtags – where users pay attention, is not random, suggesting that the process is collective.
As shown in Figure 7, adsorption decreases with increasing temperature, suggesting that the process is exothermic in nature.
Transcriptional differentiation is correlated with combinations of known and previously undefined transcription factors, suggesting that the process is tightly regulated.
The hack comes as GOP presidential candidate Donald Trump has stirred fears about election hacking, suggesting that the process could be "rigged" against him through a cyberattack.
Chlorarachniophytes are particularly interesting study objects, because these microbes still retain some of the green alga's nucleus, suggesting that the process of secondary endosymbiosis is still ongoing.
At the meeting, Sorg's group presented evidence that destroying the PNN in some regions can erase drug-associated memories, suggesting that the process may be reversible.
