Goalline technology could be used at Euro 2016 and in next season's Champions League and Europa League.
If approved, Uefa's system of positioning an additional assistant referee behind each goal would remain.
European football's governing body discussed the issue on Friday and said it would make a decision in January.
|Euro 2016 draw|
|The draw for the 24-team Euro 2016 finals takes place in Paris on Saturday. There is live coverage on BBC Two from 17:15 GMT, BBC Radio 5 live from 17:20, and on the BBC Sport website.|
At a news conference in Paris, Uefa general secretary Gianni Infantino said there was a "positive" attitude towards its implementation, despite "logistical challenges".
"This has been on the table for quite some time," he added.
"If it happens for Euro 2016 then it will also happen for the club competitions for next season, the Champions League and Europa League. This will be in addition to the five assistants.
"The final decision will be made in January but the executive committee was pretty positive in its mindset."
What about security concerns in France?
Infantino and Jacques Lambert - head of the Euro 2016 organising committee - were also asked about plans around security in light of last month's terror attacks in Paris.
"Since 13 November we have held a number of technical meetings to learn all we can about what happened at the Stade de France and around it," Lambert said.
"We have also been in contact with officials at the Ministry of the Interior, the Paris police force, security and intelligence services. The co-ordination with the state services will intensify over coming days and weeks."
Lambert also said plans to have fan zones in the 10 host cities would remain.
"For them, these are a place where crowds can gather and can see the matches for free on big screens," he said.
"It also helps to have this crowd gathered in one place rather than scattered around the towns."
More prize money as tournament expands
Uefa also announced an increase in the prize money to be distributed among teams playing at Euro 2016 in France.
The 24 teams will share a total of £217m compared to the £141m at Euro 2012 in Poland and Ukraine, which featured only 16 teams.
Each nation will receive at least £5.7m, while three wins in the group stage on the way to victory in the final would net a further £19.5m.