But Clarke said the decision to review partnerships was made at the start of the season and was not linked with the Barton incident.
"We are actively considering what our position will be and should be," Clarke, who took over as FA chairman at the start of the season, told the Times.
"I have thought about the relationship between betting and football, and alcohol and football, and I raised this at the start of the season.
"I asked for the management team to produce a report on what our position should be on a number of things, and gambling and alcohol were among those things."
The FA have commercial agreements with alcohol companies Carling, Budweiser and Carlsberg along with a long-term deal with Ladbrokes, which was agreed at the start of the current season.
Even if the FA decided to end these partnerships, there was no indication that Premier League clubs would also be prevented from having similar sponsorship deals.
"The FA will decide what is appropriate for a governing body, and there is a set of tests we would apply, and they will be different to what should apply to clubs as for a governing body they should be higher," Clarke added.
(Reporting by Hardik Vyas in Bengaluru)
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